Nothing
R/qlr.test.R
In desk: Didactic Econometrics Starter Kit
Defines functions
qlr.test
Documented in
qlr.test
qlr.test = function(mod, data = list(), from, to, sig.level = 0.05, details = FALSE){
####################################################################
#*** Hansens function to approximate p-values *********************#
####################################################################
sup_beta = function(k){
if (k == 1) beta = matrix(
c( -0.06484670, 0.99671156, 1.25732410,
-0.15305667, 0.96757645, 1.43651315,
-0.23071675, 0.95825013, 1.56531261,
-0.29247661, 0.95715782, 1.68851898,
-0.35706588, 0.95237505, 1.77889686,
-0.40514715, 0.96055795, 1.89761322,
-0.45248386, 0.95810999, 1.98370422,
-0.50458517, 0.96149538, 2.07086519,
-0.55009159, 0.96684273, 2.17244338,
-0.60241623, 0.96518399, 2.23509053,
-0.64308746, 0.97354902, 2.33722161,
-0.68833676, 0.97829106, 2.42776524,
-0.73136161, 0.98206870, 2.50833918,
-0.78078198, 0.99475319, 2.62095510,
-0.82894221, 1.00023473, 2.70286643,
-0.88430133, 1.00162529, 2.77835798,
-0.94992650, 1.00384268, 2.84325795,
-0.98828874, 1.01604712, 2.96752918,
-1.04892713, 1.02570939, 3.08442682,
-1.11527783, 1.03526033, 3.19770394,
-1.14992644, 1.06643436, 3.44739573,
-1.24010871, 1.06929468, 3.54993605,
-1.38522113, 1.06808543, 3.61667211,
-1.48296473, 1.12839690, 4.07202473,
-1.78738608, 1.17220925, 4.47267010),
25,3,byrow=TRUE)
if (k == 2) beta = matrix(
c( -0.03933112, 0.99525784, 2.44239332,
-0.14650989, 0.99386540, 2.78837829,
-0.28765583, 0.98139359, 2.93724618,
-0.35528752, 0.99427390, 3.18187129,
-0.49538961, 0.96923268, 3.19484388,
-0.58780544, 0.97339124, 3.32763253,
-0.66900489, 0.97444133, 3.44170617,
-0.77825803, 0.96678414, 3.48652761,
-0.87260977, 0.97626434, 3.61709836,
-0.96782445, 0.97636983, 3.67795020,
-1.07358977, 0.97407744, 3.71945379,
-1.12531079, 0.99897105, 3.95114475,
-1.16041007, 1.01629918, 4.14932643,
-1.29757970, 1.01526800, 4.17103882,
-1.36743697, 1.03004743, 4.32238040,
-1.43012785, 1.05139461, 4.53836755,
-1.53311747, 1.05280599, 4.61175851,
-1.65273586, 1.05932633, 4.69340428,
-1.79350728, 1.04936541, 4.68380985,
-1.91177470, 1.05884590, 4.80733540,
-2.02659329, 1.07200268, 4.97772701,
-2.18499383, 1.08674781, 5.14231666,
-2.37658580, 1.11342895, 5.40268693,
-2.51267262, 1.15305027, 5.88573096,
-3.05559851, 1.17629253, 6.11067794),
25,3,byrow=TRUE)
if (k == 3) beta = matrix(
c( -0.12508560, 0.98151496, 3.43036267,
-0.27323021, 0.98324873, 3.83943122,
-0.43148524, 0.98336371, 4.07662685,
-0.48172245, 1.00450689, 4.44796533,
-0.68989320, 0.99692978, 4.49665381,
-0.79285790, 1.00417536, 4.69772537,
-0.85066146, 1.01852003, 4.95584784,
-1.06133796, 1.00719185, 4.90812703,
-1.11977435, 1.03046019, 5.20741484,
-1.20203015, 1.03885443, 5.36939250,
-1.28736105, 1.04597379, 5.52416853,
-1.45874969, 1.03549948, 5.48885270,
-1.60889159, 1.03374376, 5.50958245,
-1.64346161, 1.06767681, 5.89426861,
-1.68334797, 1.09676432, 6.23634969,
-1.81974576, 1.10216977, 6.34122715,
-2.02648892, 1.09629880, 6.29077373,
-2.04820499, 1.13491785, 6.75208304,
-2.32304920, 1.12030935, 6.59886028,
-2.59516448, 1.09122076, 6.32294425,
-2.79776102, 1.09109337, 6.35576003,
-3.03865047, 1.09037434, 6.37212114,
-3.31299004, 1.10476754, 6.52822890,
-3.65667229, 1.13355758, 6.84167661,
-4.09174097, 1.21034051, 7.79013953),
25,3,byrow=TRUE)
if (k == 4) beta = matrix(
c( -0.40798205, 0.90528031, 3.93318971,
-0.58214849, 0.91505724, 4.41094611,
-0.67464799, 0.93646880, 4.85980413,
-0.85920669, 0.93433918, 5.01958587,
-0.99797889, 0.94119330, 5.22477986,
-1.10019761, 0.95132377, 5.46557096,
-1.24048639, 0.96334287, 5.67239340,
-1.44519417, 0.96603109, 5.73132847,
-1.43104108, 1.00890357, 6.29613628,
-1.52887344, 1.02148881, 6.51227891,
-1.66695722, 1.02616925, 6.63448592,
-1.79016819, 1.03765517, 6.82686641,
-1.91159633, 1.04392701, 6.95318158,
-1.93474222, 1.07119800, 7.36997641,
-1.94039709, 1.10122554, 7.82328663,
-2.14388035, 1.09891616, 7.83079173,
-2.34856811, 1.10457466, 7.89044965,
-2.52186324, 1.10727065, 7.95561422,
-2.81381108, 1.10513873, 7.90116455,
-3.02543477, 1.12012324, 8.08624226,
-3.33386150, 1.12405358, 8.08884313,
-3.70012182, 1.12268437, 8.00223819,
-4.08017759, 1.14201041, 8.18314656,
-4.47426188, 1.17607899, 8.60611855,
-5.32601074, 1.21390643, 8.90496643),
25,3,byrow=TRUE)
if (k == 5) beta = matrix(
c( -0.11619422, 1.02457601, 5.80252297,
-0.46546717, 1.01129094, 6.12710758,
-0.74391826, 1.00172704, 6.30619245,
-1.02744491, 0.98909190, 6.35729244,
-1.26392205, 0.98620432, 6.45912570,
-1.42145334, 0.99724660, 6.71491425,
-1.65407989, 0.99253425, 6.74047300,
-1.81536469, 1.00443530, 6.95402735,
-2.02334533, 1.00046922, 6.98677984,
-2.09938834, 1.01518764, 7.27464455,
-2.20567987, 1.02275886, 7.47265174,
-2.44943836, 1.02127435, 7.46129265,
-2.63257362, 1.01887636, 7.46907351,
-2.81161264, 1.02006744, 7.52690766,
-2.98179286, 1.03055270, 7.67224919,
-3.13342287, 1.04465740, 7.90265755,
-3.30649507, 1.05369295, 8.05397638,
-3.46464220, 1.06781143, 8.27206632,
-3.54117909, 1.10989892, 8.90945304,
-3.53272742, 1.15870693, 9.72776829,
-3.80907119, 1.17183781, 9.91294592,
-4.20676069, 1.17153767, 9.84654688,
-4.84259892, 1.14601974, 9.30420469,
-5.47685207, 1.15819167, 9.30236461,
-6.39138173, 1.17642784, 9.41930982),
25,3,byrow=TRUE)
if (k == 6) beta = matrix(
c( -0.06878690, 1.03775792, 7.09045346,
-0.33471313, 1.03320405, 7.62520471,
-0.58645046, 1.03391895, 7.96566986,
-0.84305517, 1.03864019, 8.22807265,
-1.17255237, 1.02620388, 8.19864669,
-1.46491217, 1.01747206, 8.19286900,
-1.55238215, 1.02887917, 8.53383279,
-1.79236992, 1.02880434, 8.59456107,
-1.78127768, 1.06533575, 9.26858010,
-2.21251422, 1.04598986, 8.91322396,
-2.47288843, 1.04669836, 8.92953537,
-2.61217463, 1.05733536, 9.17320934,
-2.93562547, 1.04956126, 9.00301305,
-3.34428329, 1.03025578, 8.63825734,
-3.48448133, 1.04393869, 8.87565157,
-3.64732289, 1.05837582, 9.13002628,
-3.79479594, 1.07938759, 9.47650111,
-4.04745714, 1.08339951, 9.51466537,
-4.13484904, 1.11380916, 10.08288929,
-4.27469148, 1.13359417, 10.47680321,
-4.61491387, 1.14810477, 10.64305003,
-4.91271109, 1.18479646, 11.18061590,
-5.37456783, 1.19305880, 11.24873153,
-6.01333062, 1.22140239, 11.55114952,
-7.08021496, 1.25536339, 11.84388128),
25,3,byrow=TRUE)
if (k == 7) beta = matrix(
c( -0.53689878, 0.95219603, 7.10283690,
-0.58562073, 0.98400121, 8.16310859,
-0.95896123, 0.97640322, 8.31297248,
-1.31359234, 0.97126847, 8.39458871,
-1.55985878, 0.97651275, 8.61161920,
-1.74442449, 0.99363695, 8.97007085,
-2.01759670, 0.99545856, 9.05632019,
-2.20599731, 1.00681619, 9.31295267,
-2.25783227, 1.03037828, 9.83449349,
-2.53419037, 1.02237747, 9.74010484,
-2.83535247, 1.01736263, 9.65255439,
-2.94857734, 1.03701081, 10.05826180,
-3.23125462, 1.04527054, 10.13194554,
-3.35534682, 1.07043687, 10.59763704,
-3.46151576, 1.08475765, 10.91888223,
-3.87863069, 1.07699402, 10.68834341,
-4.23908351, 1.07739268, 10.59992445,
-4.41913790, 1.10217153, 11.01503763,
-4.82113958, 1.10489462, 10.94912199,
-4.95712189, 1.14759912, 11.72034341,
-5.33535348, 1.15489501, 11.78096338,
-5.94327236, 1.14993703, 11.48022849,
-6.21449140, 1.21176160, 12.57656495,
-6.95870114, 1.21291275, 12.41746897,
-8.48837563, 1.16895303, 11.05683140),
25,3,byrow=TRUE)
if (k == 8) beta = matrix(
c( -0.06587378, 1.00259864, 9.00416324,
-0.58124366, 0.98811229, 9.29588314,
-0.53482076, 1.02737978, 10.38413127,
-0.70899479, 1.03875734, 10.86726887,
-1.07383099, 1.03945526, 10.98596388,
-1.05381577, 1.07841850, 11.87560902,
-1.27585106, 1.10005486, 12.30981590,
-1.68931537, 1.09777938, 12.24252384,
-2.18809932, 1.08874332, 12.00013658,
-2.50101866, 1.08718514, 11.97891812,
-2.85948167, 1.08365161, 11.88283066,
-3.35512723, 1.06078274, 11.38799144,
-3.65167655, 1.06322641, 11.38822596,
-4.01035186, 1.06373417, 11.32180872,
-4.24709439, 1.07465019, 11.50213594,
-4.50345226, 1.09341658, 11.80959613,
-4.90996550, 1.08551877, 11.57319597,
-5.36063931, 1.07646817, 11.25922919,
-5.73370206, 1.07605364, 11.18469963,
-6.09245707, 1.07280436, 11.07807286,
-6.46768896, 1.08010850, 11.14611701,
-6.84622409, 1.09621271, 11.40693419,
-7.23578885, 1.12575792, 11.92603449,
-7.80794405, 1.15036691, 12.32590546,
-9.19862689, 1.17118238, 12.18766263),
25,3,byrow=TRUE)
if (k == 9) beta = matrix(
c( -0.83778440, 0.93113614, 8.58838690,
-1.18727357, 0.93903334, 9.24954183,
-1.67892814, 0.93065103, 9.29685978,
-2.13655356, 0.92934556, 9.33656379,
-2.40733753, 0.94488795, 9.70552238,
-2.37013442, 0.97862192, 10.57272004,
-2.49480314, 0.99988795, 11.11202863,
-2.82625963, 0.99845236, 11.11899557,
-3.17119868, 0.99862288, 11.12620845,
-3.56365370, 0.99017086, 10.91577546,
-3.88321378, 0.99461650, 10.95270011,
-4.03132540, 1.01955132, 11.46852117,
-4.38155427, 1.01232498, 11.27876602,
-4.50039414, 1.03871207, 11.86056231,
-4.87091786, 1.03085863, 11.63335876,
-5.13839820, 1.03917618, 11.78048327,
-5.39812039, 1.05170079, 11.99793995,
-5.43335672, 1.10431373, 13.09302596,
-6.18441355, 1.06499129, 12.01561699,
-6.60044603, 1.07700965, 12.12034223,
-7.11669991, 1.08089240, 12.02669094,
-7.46755944, 1.09541073, 12.30726854,
-8.07312922, 1.10955270, 12.39994474,
-8.86841479, 1.11196659, 12.21815495,
-10.22371148, 1.13939491, 12.28861527),
25,3,byrow=TRUE)
if (k == 10) beta = matrix(
c( -0.12732608, 1.01972827, 11.23288885,
-0.77782321, 0.99827640, 11.39255875,
-1.24808905, 0.99995480, 11.66130981,
-1.76904345, 0.98955787, 11.58597271,
-2.09486459, 0.99858018, 11.87831304,
-2.30685545, 1.01743721, 12.36966797,
-2.70509677, 1.02589592, 12.51217351,
-2.92069286, 1.04951504, 13.04128558,
-3.19976180, 1.06492822, 13.38535841,
-3.63379340, 1.05272485, 13.09507410,
-4.01274834, 1.05200434, 13.03221170,
-4.50166071, 1.03350523, 12.57591029,
-4.97277337, 1.01177319, 12.03313903,
-5.21536918, 1.03214392, 12.43310006,
-5.65195302, 1.01761463, 12.01632623,
-6.06457328, 1.01623184, 11.88077482,
-6.05959360, 1.06276209, 12.97932137,
-6.46819929, 1.06017100, 12.81597962,
-6.87347962, 1.06428574, 12.80920657,
-7.25454462, 1.07640874, 12.97479282,
-7.76257167, 1.07583608, 12.81308974,
-8.18205476, 1.09754669, 13.20385908,
-8.84260296, 1.10727034, 13.19094338,
-9.55384281, 1.13929623, 13.69566019,
-11.00985153, 1.14309480, 13.27442097),
25,3,byrow=TRUE)
if (k == 11) beta = matrix(
c( -0.28687631, 0.98957614, 11.83783861,
-1.01453484, 0.96835936, 11.90975793,
-1.74016510, 0.95855704, 11.79102043,
-2.14079218, 0.97100936, 12.15587054,
-2.50789978, 0.96858600, 12.25383710,
-2.62260858, 0.99972676, 13.05242107,
-2.88704980, 1.00826291, 13.33554168,
-3.25691388, 1.01123650, 13.40020219,
-3.77111395, 1.00174976, 13.11446290,
-4.02040298, 1.01270387, 13.37818178,
-4.21877289, 1.02263415, 13.67803712,
-4.20809405, 1.06043526, 14.67639243,
-4.62395981, 1.05332870, 14.43892816,
-5.28744427, 1.03341760, 13.74971322,
-5.60464823, 1.04034926, 13.84817867,
-6.19483467, 1.01589606, 13.11638006,
-6.56252902, 1.01908267, 13.10678460,
-6.78917650, 1.03551668, 13.48939975,
-6.97852808, 1.06079144, 14.12219368,
-7.81007221, 1.01892107, 12.80828328,
-8.50886767, 0.99945890, 12.06993783,
-9.01689388, 1.01879789, 12.34966736,
-9.55606731, 1.06131659, 13.13286940,
-10.47717098, 1.06036243, 12.77710316,
-11.89998388, 1.11053955, 13.39248273),
25,3,byrow=TRUE)
if (k == 12) beta = matrix(
c( -0.20697609, 0.99318500, 13.02526679,
-1.25560706, 0.95738412, 12.61430280,
-1.38547294, 0.98877323, 13.70117093,
-1.87046797, 0.99752949, 13.97922155,
-2.32172961, 1.00261042, 14.15156668,
-2.77530991, 1.00830993, 14.27368705,
-3.42319608, 0.99496327, 13.84539441,
-3.91419160, 0.99569457, 13.77323571,
-3.98123284, 1.03266760, 14.75121929,
-4.27776907, 1.03969503, 14.92183058,
-4.10943673, 1.08139639, 16.20106765,
-4.62176712, 1.06960628, 15.83163865,
-5.31805601, 1.05319163, 15.14323043,
-5.80163800, 1.04781506, 14.88197405,
-6.31362677, 1.03917077, 14.50509125,
-6.83561824, 1.03283667, 14.18372982,
-7.27842657, 1.03422740, 14.07860787,
-7.79706943, 1.02343400, 13.63889444,
-8.24233569, 1.02377082, 13.53052355,
-8.75119040, 1.01203272, 13.11206506,
-9.26781892, 1.03507954, 13.44530299,
-9.85615645, 1.04416615, 13.45292064,
-10.35040195, 1.09166954, 14.47635207,
-11.37537184, 1.05858260, 13.31219885,
-12.87922864, 1.06208248, 12.83248868),
25,3,byrow=TRUE)
if (k == 13) beta = matrix(
c( -0.96032292, 0.96782155, 12.96494958,
-1.78562028, 0.94350733, 12.91224967,
-1.97966067, 0.96963899, 13.91086002,
-2.42158333, 0.97543310, 14.20571032,
-2.48856717, 1.00870226, 15.25854613,
-3.28051437, 0.98402078, 14.52667154,
-3.78503843, 0.99298565, 14.63233359,
-4.14403801, 1.00465319, 14.90420398,
-4.43321221, 1.01579244, 15.22639182,
-4.69094902, 1.02854159, 15.56571593,
-5.06109662, 1.03493729, 15.68524541,
-5.72733410, 1.01128328, 14.90697688,
-5.79578200, 1.04440256, 15.81532942,
-6.50909126, 1.01770567, 14.89617531,
-6.60160327, 1.05548531, 15.88779531,
-6.91561016, 1.06849333, 16.18754384,
-7.54515073, 1.06249592, 15.76113514,
-7.93078073, 1.06995710, 15.86478742,
-8.41010623, 1.08030302, 15.98357275,
-8.86495369, 1.10123141, 16.37129480,
-9.52126643, 1.09017381, 15.84531873,
-10.30207235, 1.07135898, 15.05116768,
-11.06975833, 1.07145152, 14.77495506,
-12.15664045, 1.07848089, 14.48652940,
-13.88493811, 1.09269398, 14.09406033),
25,3,byrow=TRUE)
if (k == 14) beta = matrix(
c( -0.53057890, 0.98368009, 14.62946881,
-0.80812173, 1.01109688, 16.00894877,
-1.59572361, 1.00005397, 15.88694739,
-2.19031473, 0.99792404, 15.93684770,
-2.39824582, 1.03020888, 16.90193781,
-2.75800734, 1.03961272, 17.24362728,
-3.49182845, 1.01938528, 16.59438834,
-4.05510978, 1.01959643, 16.46717786,
-4.45062227, 1.03128162, 16.72458913,
-4.75937805, 1.04463912, 17.05600286,
-5.16988136, 1.04163329, 16.95591334,
-5.77217189, 1.02954537, 16.46927443,
-5.90079070, 1.05276183, 17.16009456,
-6.28750433, 1.06353614, 17.37618590,
-6.66785584, 1.07798238, 17.64938382,
-7.29857891, 1.06357005, 17.05375164,
-7.96433421, 1.05648117, 16.58128765,
-8.54188927, 1.04729101, 16.11546709,
-8.94534315, 1.07352566, 16.69846699,
-9.35262892, 1.08488023, 16.94832682,
-9.73355542, 1.11384048, 17.67968688,
-10.52623971, 1.10944281, 17.23924469,
-11.51719761, 1.11004154, 16.80463243,
-12.35480897, 1.15898291, 17.87674562,
-14.61237001, 1.15307761, 16.55755233),
25,3,byrow=TRUE)
if (k == 15) beta = matrix(
c( -0.67396160, 0.96758770, 15.25728555,
-1.03059879, 0.98646992, 16.45491413,
-1.04906844, 1.01868047, 17.87873686,
-1.25236282, 1.04215207, 18.83215491,
-1.64262441, 1.05467658, 19.31397857,
-1.54300336, 1.09638126, 20.79452208,
-2.48260690, 1.08329937, 20.12425910,
-3.10322952, 1.08183200, 19.95277639,
-3.81410781, 1.08601992, 19.81833633,
-4.42629192, 1.08458304, 19.58738850,
-5.30936470, 1.06292778, 18.63729564,
-5.73487329, 1.06520085, 18.66118103,
-6.59234495, 1.04157247, 17.61777071,
-6.77170123, 1.06366213, 18.31681133,
-7.57864760, 1.03613103, 17.20167832,
-8.08212767, 1.04059581, 17.15999253,
-8.54406816, 1.04916238, 17.25797283,
-9.05194333, 1.05477016, 17.22576198,
-9.35900130, 1.08401132, 18.02889558,
-9.73494274, 1.10730545, 18.63943558,
-10.57869777, 1.09893801, 18.01695357,
-11.42062974, 1.09102591, 17.44317122,
-12.44191891, 1.07604096, 16.55885361,
-13.69538964, 1.06057172, 15.52893606,
-15.48531300, 1.03827923, 14.10625561),
25,3,byrow=TRUE)
if (k == 16) beta = matrix(
c( -0.09134650, 1.00135334, 17.44844463,
-1.04378984, 0.98376663, 17.48342087,
-1.96856694, 0.97066665, 17.18307302,
-2.55693634, 0.97587169, 17.39099592,
-3.48268362, 0.96434741, 16.83961037,
-3.98503866, 0.97076823, 17.00297254,
-4.68248535, 0.96454779, 16.65995197,
-4.79433839, 0.99366441, 17.63287496,
-5.22778799, 1.01098551, 18.04404405,
-5.61157139, 1.01795115, 18.19984089,
-5.77881057, 1.04350812, 19.01734887,
-6.24269823, 1.05369725, 19.19847986,
-7.00486744, 1.04041905, 18.47770031,
-7.59116740, 1.04728599, 18.44453170,
-8.17764741, 1.03465732, 17.88295181,
-8.21284923, 1.06781106, 19.04304380,
-8.56768956, 1.08294771, 19.44003984,
-9.13026570, 1.08679108, 19.32503948,
-9.38913624, 1.12271764, 20.40520153,
-10.30386897, 1.10369615, 19.39385495,
-11.01233954, 1.12282902, 19.63063480,
-11.70690938, 1.14842385, 20.12473257,
-12.26629045, 1.19537226, 21.43391832,
-13.95205351, 1.17989802, 20.06497381,
-16.33802631, 1.14691263, 17.84014338),
25,3,byrow=TRUE)
if (k == 17) beta = matrix(
c( -1.19451064, 0.96213021, 16.67034331,
-0.61304263, 1.02910449, 19.84900333,
-1.78139109, 1.00688152, 19.19472094,
-1.74865854, 1.04644760, 20.80901562,
-2.95068847, 1.01743683, 19.63995018,
-3.94648680, 1.00624209, 18.96154153,
-4.11204387, 1.03555902, 19.97354223,
-5.01078513, 1.01746947, 19.14389422,
-5.30560447, 1.04014327, 19.86179186,
-5.99452544, 1.02756756, 19.27339377,
-6.35254017, 1.04446620, 19.73926209,
-6.84941244, 1.04282184, 19.60762015,
-7.22864758, 1.05195602, 19.81835460,
-8.40745421, 1.00952605, 17.93825819,
-8.73700419, 1.03603070, 18.62634828,
-9.42296398, 1.02982490, 18.16414262,
-9.91701341, 1.04509046, 18.43859768,
-10.45110576, 1.04570811, 18.25837821,
-10.81712311, 1.07909554, 19.20599318,
-11.30777705, 1.09802480, 19.64492200,
-11.96527304, 1.10697097, 19.68717938,
-12.76105449, 1.11400431, 19.57373518,
-13.73171703, 1.14524902, 20.08927800,
-15.05430428, 1.14911289, 19.62156890,
-17.20018832, 1.15443460, 18.79900119),
25,3,byrow=TRUE)
if (k == 18) beta = matrix(
c( -0.57901589, 0.98622919, 18.77173073,
-0.61566409, 1.02219984, 20.85053838,
-1.94156883, 1.00123632, 20.04023678,
-2.62055985, 1.00211368, 20.13829144,
-2.77904140, 1.03422849, 21.37945116,
-3.57177154, 1.02910203, 21.06068346,
-4.42213185, 1.02211869, 20.57597229,
-5.10532787, 1.01642223, 20.24004620,
-5.46108672, 1.03819744, 20.90280333,
-6.46824055, 1.01047248, 19.60643024,
-6.35209946, 1.05135326, 21.18669406,
-7.19429720, 1.03651021, 20.37872334,
-7.76122523, 1.03574401, 20.15817732,
-8.09612319, 1.05605009, 20.75737492,
-8.86934521, 1.03830396, 19.85238989,
-9.24340158, 1.06235959, 20.52349087,
-9.82676851, 1.06441205, 20.37023029,
-10.62998450, 1.05028481, 19.53064308,
-11.27685859, 1.06503994, 19.72250170,
-12.03859451, 1.06183990, 19.27746128,
-12.73477308, 1.07685809, 19.45448463,
-13.40440195, 1.10629121, 20.15939105,
-14.15023958, 1.14425550, 21.17276423,
-15.65001360, 1.15140506, 20.63867090,
-18.09895960, 1.17029897, 19.96762244),
25,3,byrow=TRUE)
if (k == 19) beta = matrix(
c( -1.32304249, 0.95832919, 18.48023306,
-2.79621128, 0.93353500, 17.84287279,
-3.56766199, 0.93210709, 17.94912876,
-4.05795479, 0.94709624, 18.54127463,
-4.89711879, 0.93567098, 18.06100574,
-5.92841321, 0.91165966, 16.99663380,
-6.39059643, 0.91773957, 17.17688227,
-7.08768290, 0.91252457, 16.79805798,
-7.53083000, 0.92187570, 17.03570870,
-8.01208734, 0.92170289, 16.92467236,
-8.70797744, 0.90225855, 16.08050151,
-9.44730653, 0.88036159, 15.10697972,
-9.83731797, 0.88884871, 15.27001414,
-10.01036700, 0.92151941, 16.36094134,
-10.64602144, 0.90818127, 15.66802961,
-11.18554702, 0.89770414, 15.17074312,
-11.63296397, 0.90139634, 15.16459209,
-12.13704880, 0.90008482, 14.94170023,
-12.52353920, 0.91853667, 15.46218201,
-13.00828860, 0.92199325, 15.45235636,
-13.58216050, 0.92194461, 15.24901053,
-14.17176731, 0.94080557, 15.66519855,
-14.94024433, 0.96868608, 16.27646089,
-16.01544412, 1.01592580, 17.37790692,
-18.18744736, 1.04257134, 17.17560191),
25,3,byrow=TRUE)
if (k == 20) beta = matrix(
c( -0.93767346, 0.97989282, 20.31537415,
-1.39743879, 1.00526196, 21.87285020,
-2.78023901, 0.97254899, 20.71574061,
-3.13333051, 0.99926250, 21.81622923,
-3.69819450, 1.00898788, 22.17948485,
-4.63133758, 0.99712304, 21.55110669,
-5.05468994, 1.01308178, 22.10566166,
-5.93983376, 0.99844861, 21.32350727,
-6.51943117, 1.00599883, 21.44378380,
-7.34041405, 0.98818312, 20.55047206,
-7.87705422, 0.99043401, 20.49316663,
-8.34525685, 0.99739582, 20.64475672,
-8.86884710, 0.99682660, 20.46923537,
-9.52077570, 1.00334801, 20.41596695,
-10.19551877, 0.99669217, 19.90054772,
-10.86984218, 0.99308869, 19.50959355,
-11.59017802, 0.97738919, 18.67196064,
-12.13536344, 0.97206863, 18.31406331,
-12.88553549, 0.98125679, 18.25001052,
-13.70987004, 0.95151093, 16.87702723,
-14.26661135, 0.99125929, 17.99806101,
-15.21057964, 0.96736269, 16.73489655,
-16.08902791, 0.98651967, 17.01761330,
-17.11358176, 1.00653595, 17.31938288,
-18.99297261, 1.02028684, 16.98233441),
25,3,byrow=TRUE)
if (k == 21) beta = matrix(
c( -1.91882482, 0.94842852, 19.69796548,
-2.50977144, 0.96036523, 20.79858948,
-1.64637756, 1.03641684, 24.52136264,
-2.92698693, 1.02109845, 23.70330544,
-4.07208251, 1.01005923, 22.99022226,
-5.13694912, 0.99259316, 22.07384199,
-5.41945890, 1.01412676, 22.93456068,
-5.70365743, 1.03833275, 23.84581621,
-6.25263884, 1.04479951, 24.00468583,
-6.36733605, 1.07123783, 25.09882342,
-7.06329052, 1.07312362, 24.91325266,
-7.98139299, 1.07450508, 24.49659610,
-8.76118074, 1.07014540, 23.99932504,
-9.60618958, 1.05749547, 23.20433673,
-10.49489334, 1.04481273, 22.31128884,
-11.27740520, 1.03815847, 21.72831161,
-11.93420729, 1.03827458, 21.47099142,
-12.57665664, 1.03475703, 21.09789423,
-13.32753376, 1.04014114, 20.94560832,
-14.07700093, 1.04739527, 20.85908102,
-14.91429075, 1.05478624, 20.72634030,
-15.75739961, 1.06251211, 20.63366713,
-16.86927750, 1.05837778, 19.95358696,
-18.19943522, 1.05806746, 19.32667266,
-20.35463760, 1.02487475, 17.11170102),
25,3,byrow=TRUE)
if (k == 22) beta = matrix(
c( -1.01685430, 0.96688912, 21.98022025,
-2.60495567, 0.93597836, 21.11569491,
-2.86000663, 0.96019540, 22.45634101,
-2.68675011, 1.01025060, 24.78566589,
-1.94661764, 1.07707279, 28.08627208,
-3.48454706, 1.04456257, 26.32270605,
-3.99295200, 1.06079869, 26.87255509,
-4.97105555, 1.06472509, 26.57416348,
-4.55753010, 1.12659794, 29.37877651,
-5.45965609, 1.12532202, 28.93237653,
-6.56098097, 1.11340021, 27.95718271,
-8.38680220, 1.06099678, 24.99109955,
-8.62176424, 1.09475780, 26.22161836,
-10.14315750, 1.05136043, 23.77527362,
-11.04032773, 1.04140032, 22.94742809,
-11.45645206, 1.07058560, 23.90537726,
-12.11371089, 1.07310397, 23.73157476,
-12.76806289, 1.07068440, 23.38510717,
-13.17776800, 1.08979475, 24.05711488,
-13.99800348, 1.10274996, 24.14490565,
-14.80089189, 1.10858659, 24.02991800,
-15.89462589, 1.10743573, 23.42573753,
-17.22077668, 1.10225224, 22.54046335,
-18.72943574, 1.09611546, 21.56661458,
-21.25689814, 1.13102626, 21.55519570),
25,3,byrow=TRUE)
if (k == 23) beta = matrix(
c( 0.94096473, 1.07372683, 27.61960460,
-1.22725053, 1.02744152, 25.92215252,
-1.75872846, 1.05225294, 27.17649901,
-3.95757680, 1.00304141, 24.50457048,
-4.94110206, 0.99181473, 23.92842835,
-5.77428650, 0.99663970, 23.87169872,
-6.08848061, 1.02262192, 24.91962948,
-6.58259851, 1.03086116, 25.20980936,
-5.48128544, 1.11650316, 29.48574396,
-6.79236566, 1.09244046, 27.91271614,
-7.53943946, 1.10004847, 27.88603637,
-8.34133308, 1.10349604, 27.67781945,
-8.17356070, 1.14793429, 29.72018995,
-9.41939055, 1.12552664, 28.20998253,
-10.44472371, 1.11384156, 27.22012433,
-10.87498349, 1.13660786, 28.01731654,
-12.41061954, 1.07982337, 24.98332759,
-13.05498712, 1.09274429, 25.19280476,
-13.07771005, 1.15828445, 27.94298491,
-13.99905583, 1.15348295, 27.34964066,
-15.10380703, 1.16218820, 27.09040491,
-16.40762679, 1.14845028, 25.86970847,
-18.05996121, 1.12716807, 24.09159783,
-19.76683028, 1.09311020, 21.90394123,
-22.31185721, 1.08834724, 20.36172534),
25,3,byrow=TRUE)
if (k == 24) beta = matrix(
c( 1.08326391, 1.05535733, 28.30769774,
0.76051631, 1.08055869, 30.35395560,
2.07027863, 1.15420882, 34.90167248,
-2.10575650, 1.05432766, 28.84155289,
-3.78479942, 1.02970587, 27.21974833,
-5.13505669, 1.01490791, 26.11348070,
-6.06385571, 1.01432448, 25.77710031,
-6.79994277, 1.01889057, 25.75182208,
-8.01575875, 1.00144128, 24.53316419,
-9.00652420, 0.98843670, 23.58348620,
-9.39541502, 1.00254099, 24.12014970,
-10.37808952, 0.98496430, 23.00476986,
-11.16653768, 0.97871428, 22.39967565,
-11.82597991, 0.97385725, 21.99126271,
-12.53712013, 0.97153821, 21.57474142,
-13.31498065, 0.96309439, 20.90466170,
-13.92159257, 0.96883525, 20.89528342,
-14.51359909, 0.97639956, 20.94992826,
-15.40003703, 0.96160022, 19.95839186,
-16.13707217, 0.94646595, 19.07445895,
-16.63866207, 0.98793255, 20.53590146,
-17.60771953, 0.96687106, 19.26301167,
-18.66634280, 1.00976894, 20.40514584,
-19.83568951, 1.07633872, 22.56413126,
-22.51568418, 1.09637139, 21.91256097),
25,3,byrow=TRUE)
if (k == 25) beta = matrix(
c( -2.11162974, 0.93794913, 23.18746660,
-3.35339899, 0.93395086, 23.36705501,
-3.72841764, 0.96199485, 24.83937269,
-4.91865235, 0.94112157, 23.85012631,
-5.10718347, 0.97222478, 25.33396746,
-5.34523901, 0.99615092, 26.49773940,
-6.49950328, 0.98202759, 25.48747225,
-6.56823372, 1.01649160, 27.08610064,
-7.53743525, 1.02132776, 26.83965099,
-8.23573648, 1.02538744, 26.75434581,
-8.27526709, 1.06566549, 28.54918733,
-9.42134551, 1.04595452, 27.20979632,
-10.64615787, 1.02650382, 25.73918928,
-11.30236859, 1.03758000, 25.93585014,
-12.11073251, 1.03321785, 25.37032460,
-12.68487160, 1.05029190, 25.85223952,
-12.97665450, 1.08466360, 27.24720391,
-14.16209122, 1.04603251, 25.04274427,
-15.60464973, 0.99794254, 22.25921046,
-16.44342921, 0.99847821, 21.88312221,
-17.13809253, 1.03848496, 23.18507078,
-17.81256047, 1.08470064, 24.85988352,
-19.05804694, 1.06412860, 23.44248595,
-20.65856043, 1.08638148, 23.52732190,
-23.41820502, 1.06165219, 20.98144312),
25,3,byrow=TRUE)
if (k == 26) beta = matrix(
c( -0.05998747, 1.02982801, 28.61811868,
-0.58564982, 1.04961528, 30.38532975,
-1.39278332, 1.06454206, 31.22928765,
-3.37780497, 1.04012063, 29.47389384,
-5.80306991, 0.98378317, 26.04907108,
-6.30431193, 1.00124407, 26.78760532,
-6.64905220, 1.01380307, 27.46293864,
-7.72028924, 1.02020813, 27.18313342,
-9.77306301, 0.95922771, 23.59814373,
-9.46699714, 1.01904485, 26.43272948,
-10.44746836, 1.00004575, 25.25913836,
-11.53549458, 0.98170567, 23.98255449,
-11.51455610, 1.01813519, 25.70945692,
-12.21245714, 1.01828881, 25.46270057,
-13.33619262, 0.99253144, 23.80580119,
-13.93937444, 1.00632148, 24.16639428,
-14.13636162, 1.03724870, 25.56131431,
-15.13548602, 1.02542669, 24.51652034,
-15.12544755, 1.09007722, 27.47962222,
-16.01073023, 1.10591548, 27.72250043,
-17.45954163, 1.07588936, 25.62288587,
-18.52209521, 1.09174638, 25.77408883,
-19.96891259, 1.09508217, 25.13280835,
-21.77962654, 1.06854561, 23.03450007,
-24.37165652, 1.05183879, 20.98754102),
25,3,byrow=TRUE)
if (k == 27) beta = matrix(
c( 0.14408865, 1.01068622, 29.41328950,
-1.68824341, 0.98929663, 28.64307647,
-2.80529427, 0.98710321, 28.60200288,
-3.84471906, 0.98918892, 28.55531450,
-5.27514707, 0.97141833, 27.31581548,
-6.30987093, 0.97040265, 26.90660641,
-6.75814771, 0.99510374, 27.92165873,
-6.67078231, 1.03907408, 30.11445362,
-7.90742503, 1.02529341, 28.96859473,
-9.48244344, 0.98724672, 26.51269125,
-9.80080117, 1.01516838, 27.68474829,
-10.70348941, 1.01679016, 27.33180829,
-11.94969029, 0.99541567, 25.71194011,
-12.95847838, 0.98964061, 24.94254810,
-13.52794048, 1.00202774, 25.25357115,
-14.23377404, 1.01739432, 25.58876661,
-15.18513750, 1.00810225, 24.69139239,
-15.89245980, 1.00825698, 24.39537925,
-16.23689422, 1.05540668, 26.40052685,
-17.15303179, 1.07131004, 26.61769943,
-18.17974307, 1.07062455, 26.07177997,
-19.31726960, 1.06937314, 25.45104495,
-20.83059788, 1.05641563, 24.04909301,
-22.53758651, 1.05115003, 22.91751863,
-25.18173730, 1.04145774, 21.06003005),
25,3,byrow=TRUE)
if (k == 28) beta = matrix(
c( 0.79939887, 1.05529572, 32.44262828,
0.03205666, 1.05739119, 33.53896381,
-0.89955233, 1.06602683, 34.12554601,
-1.48570330, 1.09069306, 35.37929165,
-0.82383039, 1.14737169, 38.84664089,
0.53245320, 1.21407944, 43.34230761,
0.08803781, 1.23356150, 44.36915131,
-2.32772158, 1.20863128, 41.77712842,
-3.26635598, 1.21820913, 41.88401734,
-4.51747286, 1.21063524, 40.93437115,
-6.03001976, 1.18925759, 39.19255188,
-8.83424437, 1.12225802, 34.41082052,
-10.45716586, 1.09052552, 32.03370191,
-12.24748808, 1.05516616, 29.37133975,
-13.51362312, 1.02900233, 27.50355690,
-14.47395149, 1.02306775, 26.76722426,
-15.43533936, 1.01004287, 25.71096559,
-15.82692606, 1.04043642, 26.95265845,
-16.48073364, 1.05566763, 27.40397458,
-17.34560575, 1.07072731, 27.65472138,
-18.49748390, 1.07548152, 27.22321787,
-20.28612607, 1.01471198, 23.42269307,
-21.45173389, 1.04802042, 24.32037996,
-23.05258190, 1.04579565, 23.41133954,
-25.86459932, 1.00620908, 20.07803846),
25,3,byrow=TRUE)
if (k == 29) beta = matrix(
c( -0.97451814, 1.00251973, 30.17147365,
-3.31523561, 0.96215578, 28.27740352,
-3.44181996, 0.99687847, 30.48576952,
-4.06057325, 1.00256689, 31.01252468,
-5.50043111, 0.99230352, 30.03585883,
-5.90874636, 1.01123305, 31.00502132,
-7.37484097, 0.99460204, 29.59149220,
-8.06869210, 1.00890208, 30.02967848,
-9.19980094, 0.99060666, 28.77440772,
-9.97292626, 1.00048743, 28.87413810,
-11.33413330, 0.98179803, 27.27530692,
-11.13943081, 1.03315987, 29.98111389,
-11.51670322, 1.05219197, 30.81037166,
-12.87366330, 1.04309359, 29.57903806,
-13.55604421, 1.05344100, 29.74943841,
-14.91348471, 1.01932170, 27.46045464,
-15.87673684, 1.01992618, 26.96048751,
-16.80606996, 0.99185982, 25.28187726,
-17.25885348, 1.03676180, 27.19758151,
-17.91295160, 1.04274235, 27.27002912,
-19.27876378, 1.01724776, 25.31003597,
-20.33252371, 1.06093825, 26.73307797,
-21.67046167, 1.04904433, 25.51049744,
-23.45241774, 1.02967967, 23.64576459,
-26.34713744, 1.05793273, 23.30933223),
25,3,byrow=TRUE)
if (k == 30) beta = matrix(
c( -0.45185348, 1.01930905, 32.24298561,
-1.34552529, 1.03045829, 33.55893116,
-4.10601015, 0.97016447, 29.93683335,
-4.06956204, 0.99953822, 31.94397783,
-4.37163956, 1.02498848, 33.39057344,
-4.96136749, 1.04738273, 34.38432014,
-6.09612958, 1.04529594, 33.86332566,
-6.79175933, 1.05363440, 34.10720497,
-7.92402706, 1.05651914, 33.70380373,
-8.25906871, 1.07606786, 34.67231546,
-9.38202152, 1.07325257, 33.98238317,
-10.48079040, 1.06712586, 33.16747250,
-11.51038877, 1.07061948, 32.75282944,
-12.33853757, 1.08004765, 32.82218166,
-13.30312119, 1.08076894, 32.34345098,
-14.60679957, 1.06716915, 30.97875574,
-15.90242413, 1.04707974, 29.29035507,
-17.06116511, 1.02912412, 27.79346636,
-18.47835054, 1.00851672, 25.96976442,
-19.48334693, 1.01907055, 25.90274685,
-20.35033610, 1.02885912, 25.98118906,
-21.68959354, 1.00697161, 24.22686892,
-22.91384536, 1.03905130, 25.12327539,
-24.54026411, 1.04178393, 24.45407358,
-27.29732409, 1.03127677, 22.45845735),
25,3,byrow=TRUE)
if (k == 31) beta = matrix(
c( -3.09939971, 0.94450854, 28.18134982,
-3.32474971, 0.98336716, 31.00119845,
-3.46755751, 1.01384784, 33.16681411,
-3.41597684, 1.04100008, 35.20436783,
-5.52680707, 1.00941290, 32.79414011,
-6.65007406, 1.01476730, 32.62129883,
-6.91151910, 1.03860170, 33.96885760,
-8.55718448, 1.01869204, 32.18153230,
-9.46056864, 1.03020995, 32.35862413,
-10.04632130, 1.04674799, 32.97207244,
-11.40239801, 1.03515373, 31.67172039,
-12.74841191, 1.02136329, 30.27777146,
-13.83627077, 1.01042408, 29.19032293,
-13.75130710, 1.06808974, 32.22681722,
-14.62859882, 1.06540949, 31.70409664,
-15.42622988, 1.07090333, 31.64229513,
-16.44591320, 1.06245678, 30.73299914,
-17.15730455, 1.06704407, 30.67325888,
-18.08342986, 1.07219353, 30.49421500,
-19.34110938, 1.05514805, 28.98065367,
-20.84497913, 1.01634816, 26.22758107,
-22.05578685, 1.02356982, 25.91832218,
-23.14341564, 1.07932881, 28.10877448,
-25.17992235, 1.06481382, 26.25824622,
-27.92675759, 1.03279542, 23.24241730),
25,3,byrow=TRUE)
if (k == 32) beta = matrix(
c( 0.92283260, 1.03819509, 36.33563342,
-1.52070251, 1.01562128, 35.00865489,
-4.79973408, 0.95981872, 30.96474837,
-6.35231225, 0.94668742, 29.87536642,
-7.66478177, 0.93519189, 28.92933845,
-7.45406139, 0.98490061, 31.79056039,
-7.96374777, 1.00178787, 32.62128335,
-7.52809014, 1.05416540, 35.81015699,
-9.48652501, 1.02695236, 33.36834684,
-10.49223067, 1.03229473, 33.13463429,
-10.93823367, 1.04524242, 33.75914644,
-13.34914328, 0.98612341, 29.37050071,
-14.40618037, 0.97546849, 28.29855728,
-15.55996409, 0.95460710, 26.69707930,
-16.73233927, 0.92318283, 24.55288366,
-17.54459512, 0.91990624, 24.01960086,
-18.37462368, 0.90977204, 23.14149189,
-19.11400543, 0.90749857, 22.69150290,
-19.85087871, 0.91681340, 22.81736136,
-20.80840349, 0.90420710, 21.71806053,
-21.58905123, 0.90653965, 21.53250374,
-22.53427553, 0.94378133, 22.87046348,
-23.66102570, 1.02937840, 26.48362131,
-25.55743038, 0.99195482, 23.58169052,
-28.65939380, 1.04026978, 24.15683659),
25,3,byrow=TRUE)
if (k == 33) beta = matrix(
c( -0.67127137, 0.99575825, 34.35222758,
-2.35176782, 0.99428102, 34.49659693,
-2.56288229, 1.02614781, 36.76215260,
-5.02512960, 0.99281512, 34.04780600,
-6.11785288, 0.99467136, 33.86945457,
-7.97165633, 0.96826751, 31.69911484,
-8.82467279, 0.98460369, 32.21002835,
-8.56206391, 1.03538692, 35.22055765,
-9.42732063, 1.04021534, 35.17987817,
-11.28328634, 1.01030721, 32.56794440,
-12.13419009, 1.01871061, 32.61863328,
-11.99889194, 1.06627775, 35.36023980,
-12.58860695, 1.07757568, 35.75917151,
-14.51453528, 1.04415220, 32.86082315,
-16.01651486, 1.01338290, 30.41571859,
-17.04491345, 1.00778531, 29.60724743,
-18.10622900, 0.99955707, 28.62030614,
-19.28255657, 0.98157477, 27.04299250,
-20.38447451, 0.96440457, 25.62314147,
-21.20434180, 0.97925864, 25.99263787,
-22.28587689, 0.97032645, 24.99138617,
-23.41422487, 0.96065258, 23.93896797,
-24.64959031, 0.95483837, 23.05197415,
-26.10948832, 0.94969826, 22.11034185,
-28.82959083, 0.97151376, 21.72303575),
25,3,byrow=TRUE)
if (k == 34) beta = matrix(
c( 1.39267822, 1.06370058, 39.90446451,
2.73909431, 1.12756675, 45.68828229,
-0.30852069, 1.09131542, 42.67755711,
-0.49191557, 1.11653083, 44.62849429,
-1.06900899, 1.13066921, 45.58526881,
-4.80174038, 1.06728655, 40.08783397,
-7.74429261, 1.01914747, 35.86004532,
-8.57210051, 1.02604818, 35.96295502,
-10.15214971, 1.01737407, 34.64116979,
-11.15102586, 1.01099325, 33.89280350,
-13.64298575, 0.95574297, 29.48121395,
-14.48247672, 0.95189612, 28.96091018,
-15.35212309, 0.94566483, 28.25161906,
-16.11005408, 0.95928391, 28.58397967,
-16.94107167, 0.96591946, 28.48883403,
-17.64203321, 0.97511416, 28.67790860,
-17.96105135, 1.01770827, 30.82973139,
-18.79888981, 1.04307385, 31.66576275,
-19.76444493, 1.04704203, 31.40922243,
-21.25567826, 0.99817277, 28.04338494,
-22.65736046, 0.98169890, 26.36161115,
-23.78512985, 0.99354694, 26.39511257,
-24.86149506, 1.05134906, 28.91348082,
-26.88880413, 1.06703980, 28.57247260,
-30.13194652, 1.03332063, 24.94855681),
25,3,byrow=TRUE)
if (k == 35) beta = matrix(
c( -3.40189180, 0.92713346, 31.05989534,
-4.52188036, 0.93703071, 32.09872410,
-5.97907586, 0.93890567, 31.96003363,
-5.94712440, 0.97727174, 34.53299133,
-6.29309233, 1.00636112, 36.25124788,
-6.71089295, 1.03283419, 37.75210182,
-8.38691622, 1.02082077, 36.28591385,
-10.43531078, 0.98083830, 33.13256438,
-11.30985554, 0.99454860, 33.50225784,
-12.80509172, 0.97458461, 31.65142746,
-12.96840994, 1.01144058, 33.69945410,
-14.91752468, 0.97258099, 30.50220157,
-15.78042770, 0.97385944, 30.16328051,
-16.23102540, 1.00675003, 31.77616051,
-16.57411667, 1.02867372, 32.92383975,
-17.80722296, 1.00387999, 31.00427739,
-18.56432089, 1.01357688, 31.19720032,
-20.09211544, 0.97796504, 28.39378740,
-21.15486984, 0.97750700, 27.79854046,
-22.02891632, 0.98271510, 27.67808123,
-23.25526587, 0.99321682, 27.51721336,
-24.65449898, 0.94535835, 24.25229057,
-25.87767407, 0.97442736, 25.18649370,
-27.53979094, 0.95282744, 23.20511150,
-30.01082046, 0.91685692, 20.03361673),
25,3,byrow=TRUE)
if (k == 36) beta = matrix(
c( -2.18411218, 0.97764025, 35.24512733,
-3.42768338, 0.98643182, 36.26056059,
-2.88898683, 1.03344700, 40.03169209,
-5.03434617, 1.01504602, 38.19765183,
-7.14143228, 0.98884827, 35.87719583,
-6.44365876, 1.05228443, 40.15835641,
-7.33644084, 1.06273693, 40.47798496,
-7.81222962, 1.09281793, 42.06777372,
-8.62497252, 1.11031113, 42.75113028,
-9.09990075, 1.13092416, 43.82742713,
-10.58004470, 1.12097086, 42.48676913,
-14.26595287, 1.02527598, 34.87158717,
-15.34887785, 1.02626485, 34.32553895,
-16.54588899, 1.02936518, 33.81086542,
-17.21897182, 1.04844837, 34.54260171,
-17.95794773, 1.06766552, 35.27984344,
-19.51533257, 1.03629324, 32.67133541,
-21.06924324, 1.00404695, 29.96124787,
-22.11906531, 0.99724967, 29.08920579,
-23.30316044, 0.99065045, 28.07370235,
-24.13464440, 1.01810829, 29.19048928,
-25.23203250, 1.04075799, 29.87748229,
-26.80940751, 1.01981550, 27.88621124,
-28.70564311, 1.04320299, 28.11622613,
-32.02058598, 1.04570116, 26.33697380),
25,3,byrow=TRUE)
if (k == 37) beta = matrix(
c( 4.96237545, 1.13500821, 49.55454000,
-0.88879878, 1.04122648, 42.12503438,
-2.35069382, 1.03883689, 41.96813093,
-4.46357858, 1.02482957, 40.36943102,
-5.13472407, 1.05482149, 41.97208403,
-6.38471250, 1.05946609, 41.78295272,
-7.85452304, 1.05512345, 40.87328962,
-10.21404555, 1.01870031, 37.53836098,
-11.36819028, 1.01898786, 37.05807620,
-12.54093227, 1.01635998, 36.31816850,
-13.80958526, 1.00364988, 35.00099651,
-15.33641873, 0.99259816, 33.49444177,
-16.15654992, 0.98898087, 32.97912000,
-17.31366457, 0.97321427, 31.54195411,
-18.27791676, 0.96357086, 30.54263397,
-18.79767265, 1.00241461, 32.46396330,
-19.18523508, 1.04936796, 34.96423991,
-19.99538342, 1.06233004, 35.30122987,
-21.37968612, 1.03078730, 32.81051601,
-22.18429164, 1.06323292, 34.24800930,
-23.38539326, 1.05755696, 33.31852137,
-25.29878169, 1.02954167, 30.54026938,
-26.80995112, 1.05544122, 31.16023116,
-28.92403945, 1.02417637, 28.22207761,
-31.77850540, 0.95805763, 22.96722251),
25,3,byrow=TRUE)
if (k == 38) beta = matrix(
c( 1.33123401, 1.04574971, 43.56838471,
-1.02249003, 1.03081935, 42.69352553,
-2.60590890, 1.02960286, 42.46199624,
-5.03386748, 1.00662318, 40.13577025,
-4.84022598, 1.05826122, 43.60195097,
-5.71008884, 1.07393922, 44.31867174,
-4.23324978, 1.14228276, 49.78316782,
-5.43305024, 1.14171630, 49.31508406,
-9.38670501, 1.07417889, 42.83811659,
-12.35863658, 1.01975609, 37.80317367,
-14.76322339, 0.97448773, 33.73800017,
-15.92483383, 0.97857736, 33.31051740,
-16.79956316, 0.98478833, 33.22630913,
-18.35682673, 0.96142387, 31.00877310,
-19.29588663, 0.95928468, 30.40865036,
-20.45545504, 0.93437183, 28.43881209,
-21.45765423, 0.92444520, 27.36609083,
-22.56577441, 0.88706333, 24.70344261,
-23.31772778, 0.92662930, 26.52354799,
-24.27986692, 0.91481091, 25.40327003,
-25.38170576, 0.93972718, 26.17521882,
-26.59632792, 0.92517634, 24.73857869,
-28.01733427, 0.96703695, 26.30494308,
-29.56456700, 0.91612960, 22.70128478,
-32.70868580, 0.93850610, 22.09463252),
25,3,byrow=TRUE)
if (k == 39) beta = matrix(
c( 5.15430037, 1.11132411, 51.04502521,
3.20382719, 1.11505569, 51.51111157,
2.26579400, 1.12976198, 52.75284351,
1.70478095, 1.15960051, 54.81194369,
-0.81045339, 1.14568430, 52.72699034,
-1.09089930, 1.17497088, 54.75851856,
-7.75566411, 1.05526701, 43.23767907,
-8.63732929, 1.06811547, 43.70178295,
-7.28411605, 1.13474373, 49.02252976,
-9.11821730, 1.12306980, 47.24876375,
-10.74836959, 1.11574095, 45.87483121,
-12.43301415, 1.09709216, 43.85072076,
-12.68311992, 1.12345786, 45.48505425,
-14.60913215, 1.10825333, 43.38004215,
-15.59191441, 1.10990426, 42.99786887,
-14.73154944, 1.18937861, 48.64036596,
-16.53048259, 1.16832551, 46.29534543,
-19.45911970, 1.10764914, 40.66886396,
-20.61264100, 1.11904904, 40.73416978,
-22.83687863, 1.07512997, 36.69682239,
-23.63057252, 1.11501763, 38.72599395,
-24.48836498, 1.17656691, 42.01843505,
-26.50792922, 1.18124701, 41.09368797,
-30.20153782, 1.09323998, 33.38471226,
-33.61395119, 1.00206020, 26.05468053),
25,3,byrow=TRUE)
if (k == 40) beta = matrix(
c( -3.35130854, 0.94058360, 36.52606302,
-3.36891886, 0.97357345, 39.86827031,
-4.26561375, 0.98460810, 40.82288701,
-6.54543163, 0.95855119, 38.41130665,
-8.81898894, 0.92581528, 35.46730729,
-10.19461991, 0.92127200, 34.64407264,
-10.90426574, 0.93679164, 35.37145682,
-11.95264669, 0.93808197, 35.02176249,
-12.34848756, 0.96444992, 36.58297963,
-13.59064154, 0.96161791, 35.76037366,
-14.57419256, 0.96936248, 35.72233032,
-14.96507795, 1.01149428, 38.09322964,
-14.17737602, 1.07379663, 42.65854120,
-17.57479064, 0.99973403, 35.92893612,
-18.43607852, 1.01689985, 36.47374756,
-20.28106993, 0.98492061, 33.43948378,
-21.12463625, 1.00251086, 34.04884608,
-21.64987650, 1.05087814, 36.67969240,
-23.45913736, 1.00568101, 32.92837796,
-25.28117062, 0.96363276, 29.29840746,
-26.44477551, 0.98893741, 30.12086854,
-27.54322022, 1.00339074, 30.44677077,
-29.23967429, 0.97820963, 28.00433090,
-31.24787883, 0.98529795, 27.28218372,
-34.24072356, 0.97134889, 24.79985495),
25,3,byrow=TRUE)
beta
}
pv_sup = function(tn,k,l){
if (l<1) tau = l else tau = 1/(1+sqrt(l))
beta = sup_beta(k)
x = as.matrix(beta[,1]+beta[,2]*tn)
x = x*(x>0)
pp = 1-pchisq(x,beta[,3])
taua = (.5-tau+.01)*50
tau1 = floor(taua)
p = (tau1+1-taua)*pp[tau1] + (taua-tau1)*pp[tau1+1]
if (tau == .5) p = 1- pchisq(tn,k)
if (tau <= .01) p = pp[25]
if (tau >= .49) p = ((.5-tau)*pp[1]+(tau-.49)*(1-pchisq(tn,k)))*100
p
}
####################################################################
#***************** End of Hansens function ************************#
####################################################################
if (!inherits(mod, "formula")) { # Wenn Modell übergeben ...
mf = model.frame(mod)
X = model.matrix(terms(mod), mf)
y = model.response(model.frame(mod))
}
else { # Wenn Formel übergeben ...
mf = model.frame(mod, data = data)
y = model.response(mf)
X = model.matrix(mod, data = data)
}
n = nrow(X) # Number of observations
k = ncol(X) # Number of coefs
# Residuals
SSR = sum((lm.fit(X, y)$residuals)^2)
# Some pre-calculations
pot = from:to # Define points of time to be analyzed
npot = length(pot) # How many points of time?
chi2.stats = rep(0, npot) # Initialize vector of f.stats
k = ncol(X) # Number of parameters
tAll = length(y) # Sample sisze
if ((from < round(0.15 * tAll)) | (to > round(0.85 * tAll))) warning("Specified range is too close to borders of dataset. Test statistic looses asymptotic properties and qlr-test will be unreliable!")
if (to+1 >= tAll) stop("Specified range must end at least two periods before data set ends.")
for (i in 1:npot) {
X1 = as.matrix(X[(1:pot[i]), ])
X2 = as.matrix(X[((pot[i] + 1):tAll), ])
fit1 = lm.fit(X1, y[1:pot[i]])
fit2 = lm.fit(X2, y[((pot[i] + 1):tAll)])
u = c(fit1$residuals, fit2$residuals)
sigma2 = (sum(u^2))/(tAll - 2 * k)
chi2.stats[i] = (SSR - sum(u^2))/sigma2
}
chi2.stats = t(as.matrix(chi2.stats))
dimnames(chi2.stats) = list("", pot)
max.point = which.max(chi2.stats) + from - 1
chi2.val = max(chi2.stats)
f.stats = chi2.stats/k
f.val = chi2.val/k
cv = qlr.cv(tAll, from, to, k, sig.level)
f.crit = cv$cv.f[,2]
p.value = pv_sup(chi2.val, k, cv$lambda)
H = c(paste("No break in t = ", from,"...",to, sep = ""), paste("Some break in t = ", from,"...",to, sep = ""))
names(H) = c("H0:", "H1:")
H = t(H)
test.result = if (f.val > max(f.crit)) "rej."
else if (f.val < min(f.crit)) "not rej."
else if (f.val >= min(f.crit) & f.val <= max(f.crit)) "ambiguous, use p.value!"
results = data.frame(f.value = f.val,
lower.cv = f.crit[1],
upper.cv = f.crit[2],
p.value = p.value,
sig.level = sig.level,
H0 = test.result,
row.names = "")
out = list()
attr(out, "title") = "QLR-Test for structural breaks at unknown date"
out$hyp = H # Null and alternative hypothesis
out$results = results # Basic test results
out$chi2.stats = chi2.stats
out$f.stats = f.stats
out$f.crit = f.crit
out$p.value = p.value
out$breakpoint = max.point
out$periods = pot
out$lf.crit = cv$cv.f
out$lambda = cv$lambda
attr(out, "two.sided") = T
attr(out, "details") = if (details) {T} else {F}
attr(out, "type") = "htest"
attr(out, "test.type") = "qlrtest"
class(out) = c("desk")
return(out)
}
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desk documentation built on May 29, 2024, 6:05 a.m.
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Defines functions qlr.test
Documented in qlr.test
qlr.test = function(mod, data = list(), from, to, sig.level = 0.05, details = FALSE){
####################################################################
#*** Hansens function to approximate p-values *********************#
####################################################################
sup_beta = function(k){
if (k == 1) beta = matrix(
c( -0.06484670, 0.99671156, 1.25732410,
-0.15305667, 0.96757645, 1.43651315,
-0.23071675, 0.95825013, 1.56531261,
-0.29247661, 0.95715782, 1.68851898,
-0.35706588, 0.95237505, 1.77889686,
-0.40514715, 0.96055795, 1.89761322,
-0.45248386, 0.95810999, 1.98370422,
-0.50458517, 0.96149538, 2.07086519,
-0.55009159, 0.96684273, 2.17244338,
-0.60241623, 0.96518399, 2.23509053,
-0.64308746, 0.97354902, 2.33722161,
-0.68833676, 0.97829106, 2.42776524,
-0.73136161, 0.98206870, 2.50833918,
-0.78078198, 0.99475319, 2.62095510,
-0.82894221, 1.00023473, 2.70286643,
-0.88430133, 1.00162529, 2.77835798,
-0.94992650, 1.00384268, 2.84325795,
-0.98828874, 1.01604712, 2.96752918,
-1.04892713, 1.02570939, 3.08442682,
-1.11527783, 1.03526033, 3.19770394,
-1.14992644, 1.06643436, 3.44739573,
-1.24010871, 1.06929468, 3.54993605,
-1.38522113, 1.06808543, 3.61667211,
-1.48296473, 1.12839690, 4.07202473,
-1.78738608, 1.17220925, 4.47267010),
25,3,byrow=TRUE)
if (k == 2) beta = matrix(
c( -0.03933112, 0.99525784, 2.44239332,
-0.14650989, 0.99386540, 2.78837829,
-0.28765583, 0.98139359, 2.93724618,
-0.35528752, 0.99427390, 3.18187129,
-0.49538961, 0.96923268, 3.19484388,
-0.58780544, 0.97339124, 3.32763253,
-0.66900489, 0.97444133, 3.44170617,
-0.77825803, 0.96678414, 3.48652761,
-0.87260977, 0.97626434, 3.61709836,
-0.96782445, 0.97636983, 3.67795020,
-1.07358977, 0.97407744, 3.71945379,
-1.12531079, 0.99897105, 3.95114475,
-1.16041007, 1.01629918, 4.14932643,
-1.29757970, 1.01526800, 4.17103882,
-1.36743697, 1.03004743, 4.32238040,
-1.43012785, 1.05139461, 4.53836755,
-1.53311747, 1.05280599, 4.61175851,
-1.65273586, 1.05932633, 4.69340428,
-1.79350728, 1.04936541, 4.68380985,
-1.91177470, 1.05884590, 4.80733540,
-2.02659329, 1.07200268, 4.97772701,
-2.18499383, 1.08674781, 5.14231666,
-2.37658580, 1.11342895, 5.40268693,
-2.51267262, 1.15305027, 5.88573096,
-3.05559851, 1.17629253, 6.11067794),
25,3,byrow=TRUE)
if (k == 3) beta = matrix(
c( -0.12508560, 0.98151496, 3.43036267,
-0.27323021, 0.98324873, 3.83943122,
-0.43148524, 0.98336371, 4.07662685,
-0.48172245, 1.00450689, 4.44796533,
-0.68989320, 0.99692978, 4.49665381,
-0.79285790, 1.00417536, 4.69772537,
-0.85066146, 1.01852003, 4.95584784,
-1.06133796, 1.00719185, 4.90812703,
-1.11977435, 1.03046019, 5.20741484,
-1.20203015, 1.03885443, 5.36939250,
-1.28736105, 1.04597379, 5.52416853,
-1.45874969, 1.03549948, 5.48885270,
-1.60889159, 1.03374376, 5.50958245,
-1.64346161, 1.06767681, 5.89426861,
-1.68334797, 1.09676432, 6.23634969,
-1.81974576, 1.10216977, 6.34122715,
-2.02648892, 1.09629880, 6.29077373,
-2.04820499, 1.13491785, 6.75208304,
-2.32304920, 1.12030935, 6.59886028,
-2.59516448, 1.09122076, 6.32294425,
-2.79776102, 1.09109337, 6.35576003,
-3.03865047, 1.09037434, 6.37212114,
-3.31299004, 1.10476754, 6.52822890,
-3.65667229, 1.13355758, 6.84167661,
-4.09174097, 1.21034051, 7.79013953),
25,3,byrow=TRUE)
if (k == 4) beta = matrix(
c( -0.40798205, 0.90528031, 3.93318971,
-0.58214849, 0.91505724, 4.41094611,
-0.67464799, 0.93646880, 4.85980413,
-0.85920669, 0.93433918, 5.01958587,
-0.99797889, 0.94119330, 5.22477986,
-1.10019761, 0.95132377, 5.46557096,
-1.24048639, 0.96334287, 5.67239340,
-1.44519417, 0.96603109, 5.73132847,
-1.43104108, 1.00890357, 6.29613628,
-1.52887344, 1.02148881, 6.51227891,
-1.66695722, 1.02616925, 6.63448592,
-1.79016819, 1.03765517, 6.82686641,
-1.91159633, 1.04392701, 6.95318158,
-1.93474222, 1.07119800, 7.36997641,
-1.94039709, 1.10122554, 7.82328663,
-2.14388035, 1.09891616, 7.83079173,
-2.34856811, 1.10457466, 7.89044965,
-2.52186324, 1.10727065, 7.95561422,
-2.81381108, 1.10513873, 7.90116455,
-3.02543477, 1.12012324, 8.08624226,
-3.33386150, 1.12405358, 8.08884313,
-3.70012182, 1.12268437, 8.00223819,
-4.08017759, 1.14201041, 8.18314656,
-4.47426188, 1.17607899, 8.60611855,
-5.32601074, 1.21390643, 8.90496643),
25,3,byrow=TRUE)
if (k == 5) beta = matrix(
c( -0.11619422, 1.02457601, 5.80252297,
-0.46546717, 1.01129094, 6.12710758,
-0.74391826, 1.00172704, 6.30619245,
-1.02744491, 0.98909190, 6.35729244,
-1.26392205, 0.98620432, 6.45912570,
-1.42145334, 0.99724660, 6.71491425,
-1.65407989, 0.99253425, 6.74047300,
-1.81536469, 1.00443530, 6.95402735,
-2.02334533, 1.00046922, 6.98677984,
-2.09938834, 1.01518764, 7.27464455,
-2.20567987, 1.02275886, 7.47265174,
-2.44943836, 1.02127435, 7.46129265,
-2.63257362, 1.01887636, 7.46907351,
-2.81161264, 1.02006744, 7.52690766,
-2.98179286, 1.03055270, 7.67224919,
-3.13342287, 1.04465740, 7.90265755,
-3.30649507, 1.05369295, 8.05397638,
-3.46464220, 1.06781143, 8.27206632,
-3.54117909, 1.10989892, 8.90945304,
-3.53272742, 1.15870693, 9.72776829,
-3.80907119, 1.17183781, 9.91294592,
-4.20676069, 1.17153767, 9.84654688,
-4.84259892, 1.14601974, 9.30420469,
-5.47685207, 1.15819167, 9.30236461,
-6.39138173, 1.17642784, 9.41930982),
25,3,byrow=TRUE)
if (k == 6) beta = matrix(
c( -0.06878690, 1.03775792, 7.09045346,
-0.33471313, 1.03320405, 7.62520471,
-0.58645046, 1.03391895, 7.96566986,
-0.84305517, 1.03864019, 8.22807265,
-1.17255237, 1.02620388, 8.19864669,
-1.46491217, 1.01747206, 8.19286900,
-1.55238215, 1.02887917, 8.53383279,
-1.79236992, 1.02880434, 8.59456107,
-1.78127768, 1.06533575, 9.26858010,
-2.21251422, 1.04598986, 8.91322396,
-2.47288843, 1.04669836, 8.92953537,
-2.61217463, 1.05733536, 9.17320934,
-2.93562547, 1.04956126, 9.00301305,
-3.34428329, 1.03025578, 8.63825734,
-3.48448133, 1.04393869, 8.87565157,
-3.64732289, 1.05837582, 9.13002628,
-3.79479594, 1.07938759, 9.47650111,
-4.04745714, 1.08339951, 9.51466537,
-4.13484904, 1.11380916, 10.08288929,
-4.27469148, 1.13359417, 10.47680321,
-4.61491387, 1.14810477, 10.64305003,
-4.91271109, 1.18479646, 11.18061590,
-5.37456783, 1.19305880, 11.24873153,
-6.01333062, 1.22140239, 11.55114952,
-7.08021496, 1.25536339, 11.84388128),
25,3,byrow=TRUE)
if (k == 7) beta = matrix(
c( -0.53689878, 0.95219603, 7.10283690,
-0.58562073, 0.98400121, 8.16310859,
-0.95896123, 0.97640322, 8.31297248,
-1.31359234, 0.97126847, 8.39458871,
-1.55985878, 0.97651275, 8.61161920,
-1.74442449, 0.99363695, 8.97007085,
-2.01759670, 0.99545856, 9.05632019,
-2.20599731, 1.00681619, 9.31295267,
-2.25783227, 1.03037828, 9.83449349,
-2.53419037, 1.02237747, 9.74010484,
-2.83535247, 1.01736263, 9.65255439,
-2.94857734, 1.03701081, 10.05826180,
-3.23125462, 1.04527054, 10.13194554,
-3.35534682, 1.07043687, 10.59763704,
-3.46151576, 1.08475765, 10.91888223,
-3.87863069, 1.07699402, 10.68834341,
-4.23908351, 1.07739268, 10.59992445,
-4.41913790, 1.10217153, 11.01503763,
-4.82113958, 1.10489462, 10.94912199,
-4.95712189, 1.14759912, 11.72034341,
-5.33535348, 1.15489501, 11.78096338,
-5.94327236, 1.14993703, 11.48022849,
-6.21449140, 1.21176160, 12.57656495,
-6.95870114, 1.21291275, 12.41746897,
-8.48837563, 1.16895303, 11.05683140),
25,3,byrow=TRUE)
if (k == 8) beta = matrix(
c( -0.06587378, 1.00259864, 9.00416324,
-0.58124366, 0.98811229, 9.29588314,
-0.53482076, 1.02737978, 10.38413127,
-0.70899479, 1.03875734, 10.86726887,
-1.07383099, 1.03945526, 10.98596388,
-1.05381577, 1.07841850, 11.87560902,
-1.27585106, 1.10005486, 12.30981590,
-1.68931537, 1.09777938, 12.24252384,
-2.18809932, 1.08874332, 12.00013658,
-2.50101866, 1.08718514, 11.97891812,
-2.85948167, 1.08365161, 11.88283066,
-3.35512723, 1.06078274, 11.38799144,
-3.65167655, 1.06322641, 11.38822596,
-4.01035186, 1.06373417, 11.32180872,
-4.24709439, 1.07465019, 11.50213594,
-4.50345226, 1.09341658, 11.80959613,
-4.90996550, 1.08551877, 11.57319597,
-5.36063931, 1.07646817, 11.25922919,
-5.73370206, 1.07605364, 11.18469963,
-6.09245707, 1.07280436, 11.07807286,
-6.46768896, 1.08010850, 11.14611701,
-6.84622409, 1.09621271, 11.40693419,
-7.23578885, 1.12575792, 11.92603449,
-7.80794405, 1.15036691, 12.32590546,
-9.19862689, 1.17118238, 12.18766263),
25,3,byrow=TRUE)
if (k == 9) beta = matrix(
c( -0.83778440, 0.93113614, 8.58838690,
-1.18727357, 0.93903334, 9.24954183,
-1.67892814, 0.93065103, 9.29685978,
-2.13655356, 0.92934556, 9.33656379,
-2.40733753, 0.94488795, 9.70552238,
-2.37013442, 0.97862192, 10.57272004,
-2.49480314, 0.99988795, 11.11202863,
-2.82625963, 0.99845236, 11.11899557,
-3.17119868, 0.99862288, 11.12620845,
-3.56365370, 0.99017086, 10.91577546,
-3.88321378, 0.99461650, 10.95270011,
-4.03132540, 1.01955132, 11.46852117,
-4.38155427, 1.01232498, 11.27876602,
-4.50039414, 1.03871207, 11.86056231,
-4.87091786, 1.03085863, 11.63335876,
-5.13839820, 1.03917618, 11.78048327,
-5.39812039, 1.05170079, 11.99793995,
-5.43335672, 1.10431373, 13.09302596,
-6.18441355, 1.06499129, 12.01561699,
-6.60044603, 1.07700965, 12.12034223,
-7.11669991, 1.08089240, 12.02669094,
-7.46755944, 1.09541073, 12.30726854,
-8.07312922, 1.10955270, 12.39994474,
-8.86841479, 1.11196659, 12.21815495,
-10.22371148, 1.13939491, 12.28861527),
25,3,byrow=TRUE)
if (k == 10) beta = matrix(
c( -0.12732608, 1.01972827, 11.23288885,
-0.77782321, 0.99827640, 11.39255875,
-1.24808905, 0.99995480, 11.66130981,
-1.76904345, 0.98955787, 11.58597271,
-2.09486459, 0.99858018, 11.87831304,
-2.30685545, 1.01743721, 12.36966797,
-2.70509677, 1.02589592, 12.51217351,
-2.92069286, 1.04951504, 13.04128558,
-3.19976180, 1.06492822, 13.38535841,
-3.63379340, 1.05272485, 13.09507410,
-4.01274834, 1.05200434, 13.03221170,
-4.50166071, 1.03350523, 12.57591029,
-4.97277337, 1.01177319, 12.03313903,
-5.21536918, 1.03214392, 12.43310006,
-5.65195302, 1.01761463, 12.01632623,
-6.06457328, 1.01623184, 11.88077482,
-6.05959360, 1.06276209, 12.97932137,
-6.46819929, 1.06017100, 12.81597962,
-6.87347962, 1.06428574, 12.80920657,
-7.25454462, 1.07640874, 12.97479282,
-7.76257167, 1.07583608, 12.81308974,
-8.18205476, 1.09754669, 13.20385908,
-8.84260296, 1.10727034, 13.19094338,
-9.55384281, 1.13929623, 13.69566019,
-11.00985153, 1.14309480, 13.27442097),
25,3,byrow=TRUE)
if (k == 11) beta = matrix(
c( -0.28687631, 0.98957614, 11.83783861,
-1.01453484, 0.96835936, 11.90975793,
-1.74016510, 0.95855704, 11.79102043,
-2.14079218, 0.97100936, 12.15587054,
-2.50789978, 0.96858600, 12.25383710,
-2.62260858, 0.99972676, 13.05242107,
-2.88704980, 1.00826291, 13.33554168,
-3.25691388, 1.01123650, 13.40020219,
-3.77111395, 1.00174976, 13.11446290,
-4.02040298, 1.01270387, 13.37818178,
-4.21877289, 1.02263415, 13.67803712,
-4.20809405, 1.06043526, 14.67639243,
-4.62395981, 1.05332870, 14.43892816,
-5.28744427, 1.03341760, 13.74971322,
-5.60464823, 1.04034926, 13.84817867,
-6.19483467, 1.01589606, 13.11638006,
-6.56252902, 1.01908267, 13.10678460,
-6.78917650, 1.03551668, 13.48939975,
-6.97852808, 1.06079144, 14.12219368,
-7.81007221, 1.01892107, 12.80828328,
-8.50886767, 0.99945890, 12.06993783,
-9.01689388, 1.01879789, 12.34966736,
-9.55606731, 1.06131659, 13.13286940,
-10.47717098, 1.06036243, 12.77710316,
-11.89998388, 1.11053955, 13.39248273),
25,3,byrow=TRUE)
if (k == 12) beta = matrix(
c( -0.20697609, 0.99318500, 13.02526679,
-1.25560706, 0.95738412, 12.61430280,
-1.38547294, 0.98877323, 13.70117093,
-1.87046797, 0.99752949, 13.97922155,
-2.32172961, 1.00261042, 14.15156668,
-2.77530991, 1.00830993, 14.27368705,
-3.42319608, 0.99496327, 13.84539441,
-3.91419160, 0.99569457, 13.77323571,
-3.98123284, 1.03266760, 14.75121929,
-4.27776907, 1.03969503, 14.92183058,
-4.10943673, 1.08139639, 16.20106765,
-4.62176712, 1.06960628, 15.83163865,
-5.31805601, 1.05319163, 15.14323043,
-5.80163800, 1.04781506, 14.88197405,
-6.31362677, 1.03917077, 14.50509125,
-6.83561824, 1.03283667, 14.18372982,
-7.27842657, 1.03422740, 14.07860787,
-7.79706943, 1.02343400, 13.63889444,
-8.24233569, 1.02377082, 13.53052355,
-8.75119040, 1.01203272, 13.11206506,
-9.26781892, 1.03507954, 13.44530299,
-9.85615645, 1.04416615, 13.45292064,
-10.35040195, 1.09166954, 14.47635207,
-11.37537184, 1.05858260, 13.31219885,
-12.87922864, 1.06208248, 12.83248868),
25,3,byrow=TRUE)
if (k == 13) beta = matrix(
c( -0.96032292, 0.96782155, 12.96494958,
-1.78562028, 0.94350733, 12.91224967,
-1.97966067, 0.96963899, 13.91086002,
-2.42158333, 0.97543310, 14.20571032,
-2.48856717, 1.00870226, 15.25854613,
-3.28051437, 0.98402078, 14.52667154,
-3.78503843, 0.99298565, 14.63233359,
-4.14403801, 1.00465319, 14.90420398,
-4.43321221, 1.01579244, 15.22639182,
-4.69094902, 1.02854159, 15.56571593,
-5.06109662, 1.03493729, 15.68524541,
-5.72733410, 1.01128328, 14.90697688,
-5.79578200, 1.04440256, 15.81532942,
-6.50909126, 1.01770567, 14.89617531,
-6.60160327, 1.05548531, 15.88779531,
-6.91561016, 1.06849333, 16.18754384,
-7.54515073, 1.06249592, 15.76113514,
-7.93078073, 1.06995710, 15.86478742,
-8.41010623, 1.08030302, 15.98357275,
-8.86495369, 1.10123141, 16.37129480,
-9.52126643, 1.09017381, 15.84531873,
-10.30207235, 1.07135898, 15.05116768,
-11.06975833, 1.07145152, 14.77495506,
-12.15664045, 1.07848089, 14.48652940,
-13.88493811, 1.09269398, 14.09406033),
25,3,byrow=TRUE)
if (k == 14) beta = matrix(
c( -0.53057890, 0.98368009, 14.62946881,
-0.80812173, 1.01109688, 16.00894877,
-1.59572361, 1.00005397, 15.88694739,
-2.19031473, 0.99792404, 15.93684770,
-2.39824582, 1.03020888, 16.90193781,
-2.75800734, 1.03961272, 17.24362728,
-3.49182845, 1.01938528, 16.59438834,
-4.05510978, 1.01959643, 16.46717786,
-4.45062227, 1.03128162, 16.72458913,
-4.75937805, 1.04463912, 17.05600286,
-5.16988136, 1.04163329, 16.95591334,
-5.77217189, 1.02954537, 16.46927443,
-5.90079070, 1.05276183, 17.16009456,
-6.28750433, 1.06353614, 17.37618590,
-6.66785584, 1.07798238, 17.64938382,
-7.29857891, 1.06357005, 17.05375164,
-7.96433421, 1.05648117, 16.58128765,
-8.54188927, 1.04729101, 16.11546709,
-8.94534315, 1.07352566, 16.69846699,
-9.35262892, 1.08488023, 16.94832682,
-9.73355542, 1.11384048, 17.67968688,
-10.52623971, 1.10944281, 17.23924469,
-11.51719761, 1.11004154, 16.80463243,
-12.35480897, 1.15898291, 17.87674562,
-14.61237001, 1.15307761, 16.55755233),
25,3,byrow=TRUE)
if (k == 15) beta = matrix(
c( -0.67396160, 0.96758770, 15.25728555,
-1.03059879, 0.98646992, 16.45491413,
-1.04906844, 1.01868047, 17.87873686,
-1.25236282, 1.04215207, 18.83215491,
-1.64262441, 1.05467658, 19.31397857,
-1.54300336, 1.09638126, 20.79452208,
-2.48260690, 1.08329937, 20.12425910,
-3.10322952, 1.08183200, 19.95277639,
-3.81410781, 1.08601992, 19.81833633,
-4.42629192, 1.08458304, 19.58738850,
-5.30936470, 1.06292778, 18.63729564,
-5.73487329, 1.06520085, 18.66118103,
-6.59234495, 1.04157247, 17.61777071,
-6.77170123, 1.06366213, 18.31681133,
-7.57864760, 1.03613103, 17.20167832,
-8.08212767, 1.04059581, 17.15999253,
-8.54406816, 1.04916238, 17.25797283,
-9.05194333, 1.05477016, 17.22576198,
-9.35900130, 1.08401132, 18.02889558,
-9.73494274, 1.10730545, 18.63943558,
-10.57869777, 1.09893801, 18.01695357,
-11.42062974, 1.09102591, 17.44317122,
-12.44191891, 1.07604096, 16.55885361,
-13.69538964, 1.06057172, 15.52893606,
-15.48531300, 1.03827923, 14.10625561),
25,3,byrow=TRUE)
if (k == 16) beta = matrix(
c( -0.09134650, 1.00135334, 17.44844463,
-1.04378984, 0.98376663, 17.48342087,
-1.96856694, 0.97066665, 17.18307302,
-2.55693634, 0.97587169, 17.39099592,
-3.48268362, 0.96434741, 16.83961037,
-3.98503866, 0.97076823, 17.00297254,
-4.68248535, 0.96454779, 16.65995197,
-4.79433839, 0.99366441, 17.63287496,
-5.22778799, 1.01098551, 18.04404405,
-5.61157139, 1.01795115, 18.19984089,
-5.77881057, 1.04350812, 19.01734887,
-6.24269823, 1.05369725, 19.19847986,
-7.00486744, 1.04041905, 18.47770031,
-7.59116740, 1.04728599, 18.44453170,
-8.17764741, 1.03465732, 17.88295181,
-8.21284923, 1.06781106, 19.04304380,
-8.56768956, 1.08294771, 19.44003984,
-9.13026570, 1.08679108, 19.32503948,
-9.38913624, 1.12271764, 20.40520153,
-10.30386897, 1.10369615, 19.39385495,
-11.01233954, 1.12282902, 19.63063480,
-11.70690938, 1.14842385, 20.12473257,
-12.26629045, 1.19537226, 21.43391832,
-13.95205351, 1.17989802, 20.06497381,
-16.33802631, 1.14691263, 17.84014338),
25,3,byrow=TRUE)
if (k == 17) beta = matrix(
c( -1.19451064, 0.96213021, 16.67034331,
-0.61304263, 1.02910449, 19.84900333,
-1.78139109, 1.00688152, 19.19472094,
-1.74865854, 1.04644760, 20.80901562,
-2.95068847, 1.01743683, 19.63995018,
-3.94648680, 1.00624209, 18.96154153,
-4.11204387, 1.03555902, 19.97354223,
-5.01078513, 1.01746947, 19.14389422,
-5.30560447, 1.04014327, 19.86179186,
-5.99452544, 1.02756756, 19.27339377,
-6.35254017, 1.04446620, 19.73926209,
-6.84941244, 1.04282184, 19.60762015,
-7.22864758, 1.05195602, 19.81835460,
-8.40745421, 1.00952605, 17.93825819,
-8.73700419, 1.03603070, 18.62634828,
-9.42296398, 1.02982490, 18.16414262,
-9.91701341, 1.04509046, 18.43859768,
-10.45110576, 1.04570811, 18.25837821,
-10.81712311, 1.07909554, 19.20599318,
-11.30777705, 1.09802480, 19.64492200,
-11.96527304, 1.10697097, 19.68717938,
-12.76105449, 1.11400431, 19.57373518,
-13.73171703, 1.14524902, 20.08927800,
-15.05430428, 1.14911289, 19.62156890,
-17.20018832, 1.15443460, 18.79900119),
25,3,byrow=TRUE)
if (k == 18) beta = matrix(
c( -0.57901589, 0.98622919, 18.77173073,
-0.61566409, 1.02219984, 20.85053838,
-1.94156883, 1.00123632, 20.04023678,
-2.62055985, 1.00211368, 20.13829144,
-2.77904140, 1.03422849, 21.37945116,
-3.57177154, 1.02910203, 21.06068346,
-4.42213185, 1.02211869, 20.57597229,
-5.10532787, 1.01642223, 20.24004620,
-5.46108672, 1.03819744, 20.90280333,
-6.46824055, 1.01047248, 19.60643024,
-6.35209946, 1.05135326, 21.18669406,
-7.19429720, 1.03651021, 20.37872334,
-7.76122523, 1.03574401, 20.15817732,
-8.09612319, 1.05605009, 20.75737492,
-8.86934521, 1.03830396, 19.85238989,
-9.24340158, 1.06235959, 20.52349087,
-9.82676851, 1.06441205, 20.37023029,
-10.62998450, 1.05028481, 19.53064308,
-11.27685859, 1.06503994, 19.72250170,
-12.03859451, 1.06183990, 19.27746128,
-12.73477308, 1.07685809, 19.45448463,
-13.40440195, 1.10629121, 20.15939105,
-14.15023958, 1.14425550, 21.17276423,
-15.65001360, 1.15140506, 20.63867090,
-18.09895960, 1.17029897, 19.96762244),
25,3,byrow=TRUE)
if (k == 19) beta = matrix(
c( -1.32304249, 0.95832919, 18.48023306,
-2.79621128, 0.93353500, 17.84287279,
-3.56766199, 0.93210709, 17.94912876,
-4.05795479, 0.94709624, 18.54127463,
-4.89711879, 0.93567098, 18.06100574,
-5.92841321, 0.91165966, 16.99663380,
-6.39059643, 0.91773957, 17.17688227,
-7.08768290, 0.91252457, 16.79805798,
-7.53083000, 0.92187570, 17.03570870,
-8.01208734, 0.92170289, 16.92467236,
-8.70797744, 0.90225855, 16.08050151,
-9.44730653, 0.88036159, 15.10697972,
-9.83731797, 0.88884871, 15.27001414,
-10.01036700, 0.92151941, 16.36094134,
-10.64602144, 0.90818127, 15.66802961,
-11.18554702, 0.89770414, 15.17074312,
-11.63296397, 0.90139634, 15.16459209,
-12.13704880, 0.90008482, 14.94170023,
-12.52353920, 0.91853667, 15.46218201,
-13.00828860, 0.92199325, 15.45235636,
-13.58216050, 0.92194461, 15.24901053,
-14.17176731, 0.94080557, 15.66519855,
-14.94024433, 0.96868608, 16.27646089,
-16.01544412, 1.01592580, 17.37790692,
-18.18744736, 1.04257134, 17.17560191),
25,3,byrow=TRUE)
if (k == 20) beta = matrix(
c( -0.93767346, 0.97989282, 20.31537415,
-1.39743879, 1.00526196, 21.87285020,
-2.78023901, 0.97254899, 20.71574061,
-3.13333051, 0.99926250, 21.81622923,
-3.69819450, 1.00898788, 22.17948485,
-4.63133758, 0.99712304, 21.55110669,
-5.05468994, 1.01308178, 22.10566166,
-5.93983376, 0.99844861, 21.32350727,
-6.51943117, 1.00599883, 21.44378380,
-7.34041405, 0.98818312, 20.55047206,
-7.87705422, 0.99043401, 20.49316663,
-8.34525685, 0.99739582, 20.64475672,
-8.86884710, 0.99682660, 20.46923537,
-9.52077570, 1.00334801, 20.41596695,
-10.19551877, 0.99669217, 19.90054772,
-10.86984218, 0.99308869, 19.50959355,
-11.59017802, 0.97738919, 18.67196064,
-12.13536344, 0.97206863, 18.31406331,
-12.88553549, 0.98125679, 18.25001052,
-13.70987004, 0.95151093, 16.87702723,
-14.26661135, 0.99125929, 17.99806101,
-15.21057964, 0.96736269, 16.73489655,
-16.08902791, 0.98651967, 17.01761330,
-17.11358176, 1.00653595, 17.31938288,
-18.99297261, 1.02028684, 16.98233441),
25,3,byrow=TRUE)
if (k == 21) beta = matrix(
c( -1.91882482, 0.94842852, 19.69796548,
-2.50977144, 0.96036523, 20.79858948,
-1.64637756, 1.03641684, 24.52136264,
-2.92698693, 1.02109845, 23.70330544,
-4.07208251, 1.01005923, 22.99022226,
-5.13694912, 0.99259316, 22.07384199,
-5.41945890, 1.01412676, 22.93456068,
-5.70365743, 1.03833275, 23.84581621,
-6.25263884, 1.04479951, 24.00468583,
-6.36733605, 1.07123783, 25.09882342,
-7.06329052, 1.07312362, 24.91325266,
-7.98139299, 1.07450508, 24.49659610,
-8.76118074, 1.07014540, 23.99932504,
-9.60618958, 1.05749547, 23.20433673,
-10.49489334, 1.04481273, 22.31128884,
-11.27740520, 1.03815847, 21.72831161,
-11.93420729, 1.03827458, 21.47099142,
-12.57665664, 1.03475703, 21.09789423,
-13.32753376, 1.04014114, 20.94560832,
-14.07700093, 1.04739527, 20.85908102,
-14.91429075, 1.05478624, 20.72634030,
-15.75739961, 1.06251211, 20.63366713,
-16.86927750, 1.05837778, 19.95358696,
-18.19943522, 1.05806746, 19.32667266,
-20.35463760, 1.02487475, 17.11170102),
25,3,byrow=TRUE)
if (k == 22) beta = matrix(
c( -1.01685430, 0.96688912, 21.98022025,
-2.60495567, 0.93597836, 21.11569491,
-2.86000663, 0.96019540, 22.45634101,
-2.68675011, 1.01025060, 24.78566589,
-1.94661764, 1.07707279, 28.08627208,
-3.48454706, 1.04456257, 26.32270605,
-3.99295200, 1.06079869, 26.87255509,
-4.97105555, 1.06472509, 26.57416348,
-4.55753010, 1.12659794, 29.37877651,
-5.45965609, 1.12532202, 28.93237653,
-6.56098097, 1.11340021, 27.95718271,
-8.38680220, 1.06099678, 24.99109955,
-8.62176424, 1.09475780, 26.22161836,
-10.14315750, 1.05136043, 23.77527362,
-11.04032773, 1.04140032, 22.94742809,
-11.45645206, 1.07058560, 23.90537726,
-12.11371089, 1.07310397, 23.73157476,
-12.76806289, 1.07068440, 23.38510717,
-13.17776800, 1.08979475, 24.05711488,
-13.99800348, 1.10274996, 24.14490565,
-14.80089189, 1.10858659, 24.02991800,
-15.89462589, 1.10743573, 23.42573753,
-17.22077668, 1.10225224, 22.54046335,
-18.72943574, 1.09611546, 21.56661458,
-21.25689814, 1.13102626, 21.55519570),
25,3,byrow=TRUE)
if (k == 23) beta = matrix(
c( 0.94096473, 1.07372683, 27.61960460,
-1.22725053, 1.02744152, 25.92215252,
-1.75872846, 1.05225294, 27.17649901,
-3.95757680, 1.00304141, 24.50457048,
-4.94110206, 0.99181473, 23.92842835,
-5.77428650, 0.99663970, 23.87169872,
-6.08848061, 1.02262192, 24.91962948,
-6.58259851, 1.03086116, 25.20980936,
-5.48128544, 1.11650316, 29.48574396,
-6.79236566, 1.09244046, 27.91271614,
-7.53943946, 1.10004847, 27.88603637,
-8.34133308, 1.10349604, 27.67781945,
-8.17356070, 1.14793429, 29.72018995,
-9.41939055, 1.12552664, 28.20998253,
-10.44472371, 1.11384156, 27.22012433,
-10.87498349, 1.13660786, 28.01731654,
-12.41061954, 1.07982337, 24.98332759,
-13.05498712, 1.09274429, 25.19280476,
-13.07771005, 1.15828445, 27.94298491,
-13.99905583, 1.15348295, 27.34964066,
-15.10380703, 1.16218820, 27.09040491,
-16.40762679, 1.14845028, 25.86970847,
-18.05996121, 1.12716807, 24.09159783,
-19.76683028, 1.09311020, 21.90394123,
-22.31185721, 1.08834724, 20.36172534),
25,3,byrow=TRUE)
if (k == 24) beta = matrix(
c( 1.08326391, 1.05535733, 28.30769774,
0.76051631, 1.08055869, 30.35395560,
2.07027863, 1.15420882, 34.90167248,
-2.10575650, 1.05432766, 28.84155289,
-3.78479942, 1.02970587, 27.21974833,
-5.13505669, 1.01490791, 26.11348070,
-6.06385571, 1.01432448, 25.77710031,
-6.79994277, 1.01889057, 25.75182208,
-8.01575875, 1.00144128, 24.53316419,
-9.00652420, 0.98843670, 23.58348620,
-9.39541502, 1.00254099, 24.12014970,
-10.37808952, 0.98496430, 23.00476986,
-11.16653768, 0.97871428, 22.39967565,
-11.82597991, 0.97385725, 21.99126271,
-12.53712013, 0.97153821, 21.57474142,
-13.31498065, 0.96309439, 20.90466170,
-13.92159257, 0.96883525, 20.89528342,
-14.51359909, 0.97639956, 20.94992826,
-15.40003703, 0.96160022, 19.95839186,
-16.13707217, 0.94646595, 19.07445895,
-16.63866207, 0.98793255, 20.53590146,
-17.60771953, 0.96687106, 19.26301167,
-18.66634280, 1.00976894, 20.40514584,
-19.83568951, 1.07633872, 22.56413126,
-22.51568418, 1.09637139, 21.91256097),
25,3,byrow=TRUE)
if (k == 25) beta = matrix(
c( -2.11162974, 0.93794913, 23.18746660,
-3.35339899, 0.93395086, 23.36705501,
-3.72841764, 0.96199485, 24.83937269,
-4.91865235, 0.94112157, 23.85012631,
-5.10718347, 0.97222478, 25.33396746,
-5.34523901, 0.99615092, 26.49773940,
-6.49950328, 0.98202759, 25.48747225,
-6.56823372, 1.01649160, 27.08610064,
-7.53743525, 1.02132776, 26.83965099,
-8.23573648, 1.02538744, 26.75434581,
-8.27526709, 1.06566549, 28.54918733,
-9.42134551, 1.04595452, 27.20979632,
-10.64615787, 1.02650382, 25.73918928,
-11.30236859, 1.03758000, 25.93585014,
-12.11073251, 1.03321785, 25.37032460,
-12.68487160, 1.05029190, 25.85223952,
-12.97665450, 1.08466360, 27.24720391,
-14.16209122, 1.04603251, 25.04274427,
-15.60464973, 0.99794254, 22.25921046,
-16.44342921, 0.99847821, 21.88312221,
-17.13809253, 1.03848496, 23.18507078,
-17.81256047, 1.08470064, 24.85988352,
-19.05804694, 1.06412860, 23.44248595,
-20.65856043, 1.08638148, 23.52732190,
-23.41820502, 1.06165219, 20.98144312),
25,3,byrow=TRUE)
if (k == 26) beta = matrix(
c( -0.05998747, 1.02982801, 28.61811868,
-0.58564982, 1.04961528, 30.38532975,
-1.39278332, 1.06454206, 31.22928765,
-3.37780497, 1.04012063, 29.47389384,
-5.80306991, 0.98378317, 26.04907108,
-6.30431193, 1.00124407, 26.78760532,
-6.64905220, 1.01380307, 27.46293864,
-7.72028924, 1.02020813, 27.18313342,
-9.77306301, 0.95922771, 23.59814373,
-9.46699714, 1.01904485, 26.43272948,
-10.44746836, 1.00004575, 25.25913836,
-11.53549458, 0.98170567, 23.98255449,
-11.51455610, 1.01813519, 25.70945692,
-12.21245714, 1.01828881, 25.46270057,
-13.33619262, 0.99253144, 23.80580119,
-13.93937444, 1.00632148, 24.16639428,
-14.13636162, 1.03724870, 25.56131431,
-15.13548602, 1.02542669, 24.51652034,
-15.12544755, 1.09007722, 27.47962222,
-16.01073023, 1.10591548, 27.72250043,
-17.45954163, 1.07588936, 25.62288587,
-18.52209521, 1.09174638, 25.77408883,
-19.96891259, 1.09508217, 25.13280835,
-21.77962654, 1.06854561, 23.03450007,
-24.37165652, 1.05183879, 20.98754102),
25,3,byrow=TRUE)
if (k == 27) beta = matrix(
c( 0.14408865, 1.01068622, 29.41328950,
-1.68824341, 0.98929663, 28.64307647,
-2.80529427, 0.98710321, 28.60200288,
-3.84471906, 0.98918892, 28.55531450,
-5.27514707, 0.97141833, 27.31581548,
-6.30987093, 0.97040265, 26.90660641,
-6.75814771, 0.99510374, 27.92165873,
-6.67078231, 1.03907408, 30.11445362,
-7.90742503, 1.02529341, 28.96859473,
-9.48244344, 0.98724672, 26.51269125,
-9.80080117, 1.01516838, 27.68474829,
-10.70348941, 1.01679016, 27.33180829,
-11.94969029, 0.99541567, 25.71194011,
-12.95847838, 0.98964061, 24.94254810,
-13.52794048, 1.00202774, 25.25357115,
-14.23377404, 1.01739432, 25.58876661,
-15.18513750, 1.00810225, 24.69139239,
-15.89245980, 1.00825698, 24.39537925,
-16.23689422, 1.05540668, 26.40052685,
-17.15303179, 1.07131004, 26.61769943,
-18.17974307, 1.07062455, 26.07177997,
-19.31726960, 1.06937314, 25.45104495,
-20.83059788, 1.05641563, 24.04909301,
-22.53758651, 1.05115003, 22.91751863,
-25.18173730, 1.04145774, 21.06003005),
25,3,byrow=TRUE)
if (k == 28) beta = matrix(
c( 0.79939887, 1.05529572, 32.44262828,
0.03205666, 1.05739119, 33.53896381,
-0.89955233, 1.06602683, 34.12554601,
-1.48570330, 1.09069306, 35.37929165,
-0.82383039, 1.14737169, 38.84664089,
0.53245320, 1.21407944, 43.34230761,
0.08803781, 1.23356150, 44.36915131,
-2.32772158, 1.20863128, 41.77712842,
-3.26635598, 1.21820913, 41.88401734,
-4.51747286, 1.21063524, 40.93437115,
-6.03001976, 1.18925759, 39.19255188,
-8.83424437, 1.12225802, 34.41082052,
-10.45716586, 1.09052552, 32.03370191,
-12.24748808, 1.05516616, 29.37133975,
-13.51362312, 1.02900233, 27.50355690,
-14.47395149, 1.02306775, 26.76722426,
-15.43533936, 1.01004287, 25.71096559,
-15.82692606, 1.04043642, 26.95265845,
-16.48073364, 1.05566763, 27.40397458,
-17.34560575, 1.07072731, 27.65472138,
-18.49748390, 1.07548152, 27.22321787,
-20.28612607, 1.01471198, 23.42269307,
-21.45173389, 1.04802042, 24.32037996,
-23.05258190, 1.04579565, 23.41133954,
-25.86459932, 1.00620908, 20.07803846),
25,3,byrow=TRUE)
if (k == 29) beta = matrix(
c( -0.97451814, 1.00251973, 30.17147365,
-3.31523561, 0.96215578, 28.27740352,
-3.44181996, 0.99687847, 30.48576952,
-4.06057325, 1.00256689, 31.01252468,
-5.50043111, 0.99230352, 30.03585883,
-5.90874636, 1.01123305, 31.00502132,
-7.37484097, 0.99460204, 29.59149220,
-8.06869210, 1.00890208, 30.02967848,
-9.19980094, 0.99060666, 28.77440772,
-9.97292626, 1.00048743, 28.87413810,
-11.33413330, 0.98179803, 27.27530692,
-11.13943081, 1.03315987, 29.98111389,
-11.51670322, 1.05219197, 30.81037166,
-12.87366330, 1.04309359, 29.57903806,
-13.55604421, 1.05344100, 29.74943841,
-14.91348471, 1.01932170, 27.46045464,
-15.87673684, 1.01992618, 26.96048751,
-16.80606996, 0.99185982, 25.28187726,
-17.25885348, 1.03676180, 27.19758151,
-17.91295160, 1.04274235, 27.27002912,
-19.27876378, 1.01724776, 25.31003597,
-20.33252371, 1.06093825, 26.73307797,
-21.67046167, 1.04904433, 25.51049744,
-23.45241774, 1.02967967, 23.64576459,
-26.34713744, 1.05793273, 23.30933223),
25,3,byrow=TRUE)
if (k == 30) beta = matrix(
c( -0.45185348, 1.01930905, 32.24298561,
-1.34552529, 1.03045829, 33.55893116,
-4.10601015, 0.97016447, 29.93683335,
-4.06956204, 0.99953822, 31.94397783,
-4.37163956, 1.02498848, 33.39057344,
-4.96136749, 1.04738273, 34.38432014,
-6.09612958, 1.04529594, 33.86332566,
-6.79175933, 1.05363440, 34.10720497,
-7.92402706, 1.05651914, 33.70380373,
-8.25906871, 1.07606786, 34.67231546,
-9.38202152, 1.07325257, 33.98238317,
-10.48079040, 1.06712586, 33.16747250,
-11.51038877, 1.07061948, 32.75282944,
-12.33853757, 1.08004765, 32.82218166,
-13.30312119, 1.08076894, 32.34345098,
-14.60679957, 1.06716915, 30.97875574,
-15.90242413, 1.04707974, 29.29035507,
-17.06116511, 1.02912412, 27.79346636,
-18.47835054, 1.00851672, 25.96976442,
-19.48334693, 1.01907055, 25.90274685,
-20.35033610, 1.02885912, 25.98118906,
-21.68959354, 1.00697161, 24.22686892,
-22.91384536, 1.03905130, 25.12327539,
-24.54026411, 1.04178393, 24.45407358,
-27.29732409, 1.03127677, 22.45845735),
25,3,byrow=TRUE)
if (k == 31) beta = matrix(
c( -3.09939971, 0.94450854, 28.18134982,
-3.32474971, 0.98336716, 31.00119845,
-3.46755751, 1.01384784, 33.16681411,
-3.41597684, 1.04100008, 35.20436783,
-5.52680707, 1.00941290, 32.79414011,
-6.65007406, 1.01476730, 32.62129883,
-6.91151910, 1.03860170, 33.96885760,
-8.55718448, 1.01869204, 32.18153230,
-9.46056864, 1.03020995, 32.35862413,
-10.04632130, 1.04674799, 32.97207244,
-11.40239801, 1.03515373, 31.67172039,
-12.74841191, 1.02136329, 30.27777146,
-13.83627077, 1.01042408, 29.19032293,
-13.75130710, 1.06808974, 32.22681722,
-14.62859882, 1.06540949, 31.70409664,
-15.42622988, 1.07090333, 31.64229513,
-16.44591320, 1.06245678, 30.73299914,
-17.15730455, 1.06704407, 30.67325888,
-18.08342986, 1.07219353, 30.49421500,
-19.34110938, 1.05514805, 28.98065367,
-20.84497913, 1.01634816, 26.22758107,
-22.05578685, 1.02356982, 25.91832218,
-23.14341564, 1.07932881, 28.10877448,
-25.17992235, 1.06481382, 26.25824622,
-27.92675759, 1.03279542, 23.24241730),
25,3,byrow=TRUE)
if (k == 32) beta = matrix(
c( 0.92283260, 1.03819509, 36.33563342,
-1.52070251, 1.01562128, 35.00865489,
-4.79973408, 0.95981872, 30.96474837,
-6.35231225, 0.94668742, 29.87536642,
-7.66478177, 0.93519189, 28.92933845,
-7.45406139, 0.98490061, 31.79056039,
-7.96374777, 1.00178787, 32.62128335,
-7.52809014, 1.05416540, 35.81015699,
-9.48652501, 1.02695236, 33.36834684,
-10.49223067, 1.03229473, 33.13463429,
-10.93823367, 1.04524242, 33.75914644,
-13.34914328, 0.98612341, 29.37050071,
-14.40618037, 0.97546849, 28.29855728,
-15.55996409, 0.95460710, 26.69707930,
-16.73233927, 0.92318283, 24.55288366,
-17.54459512, 0.91990624, 24.01960086,
-18.37462368, 0.90977204, 23.14149189,
-19.11400543, 0.90749857, 22.69150290,
-19.85087871, 0.91681340, 22.81736136,
-20.80840349, 0.90420710, 21.71806053,
-21.58905123, 0.90653965, 21.53250374,
-22.53427553, 0.94378133, 22.87046348,
-23.66102570, 1.02937840, 26.48362131,
-25.55743038, 0.99195482, 23.58169052,
-28.65939380, 1.04026978, 24.15683659),
25,3,byrow=TRUE)
if (k == 33) beta = matrix(
c( -0.67127137, 0.99575825, 34.35222758,
-2.35176782, 0.99428102, 34.49659693,
-2.56288229, 1.02614781, 36.76215260,
-5.02512960, 0.99281512, 34.04780600,
-6.11785288, 0.99467136, 33.86945457,
-7.97165633, 0.96826751, 31.69911484,
-8.82467279, 0.98460369, 32.21002835,
-8.56206391, 1.03538692, 35.22055765,
-9.42732063, 1.04021534, 35.17987817,
-11.28328634, 1.01030721, 32.56794440,
-12.13419009, 1.01871061, 32.61863328,
-11.99889194, 1.06627775, 35.36023980,
-12.58860695, 1.07757568, 35.75917151,
-14.51453528, 1.04415220, 32.86082315,
-16.01651486, 1.01338290, 30.41571859,
-17.04491345, 1.00778531, 29.60724743,
-18.10622900, 0.99955707, 28.62030614,
-19.28255657, 0.98157477, 27.04299250,
-20.38447451, 0.96440457, 25.62314147,
-21.20434180, 0.97925864, 25.99263787,
-22.28587689, 0.97032645, 24.99138617,
-23.41422487, 0.96065258, 23.93896797,
-24.64959031, 0.95483837, 23.05197415,
-26.10948832, 0.94969826, 22.11034185,
-28.82959083, 0.97151376, 21.72303575),
25,3,byrow=TRUE)
if (k == 34) beta = matrix(
c( 1.39267822, 1.06370058, 39.90446451,
2.73909431, 1.12756675, 45.68828229,
-0.30852069, 1.09131542, 42.67755711,
-0.49191557, 1.11653083, 44.62849429,
-1.06900899, 1.13066921, 45.58526881,
-4.80174038, 1.06728655, 40.08783397,
-7.74429261, 1.01914747, 35.86004532,
-8.57210051, 1.02604818, 35.96295502,
-10.15214971, 1.01737407, 34.64116979,
-11.15102586, 1.01099325, 33.89280350,
-13.64298575, 0.95574297, 29.48121395,
-14.48247672, 0.95189612, 28.96091018,
-15.35212309, 0.94566483, 28.25161906,
-16.11005408, 0.95928391, 28.58397967,
-16.94107167, 0.96591946, 28.48883403,
-17.64203321, 0.97511416, 28.67790860,
-17.96105135, 1.01770827, 30.82973139,
-18.79888981, 1.04307385, 31.66576275,
-19.76444493, 1.04704203, 31.40922243,
-21.25567826, 0.99817277, 28.04338494,
-22.65736046, 0.98169890, 26.36161115,
-23.78512985, 0.99354694, 26.39511257,
-24.86149506, 1.05134906, 28.91348082,
-26.88880413, 1.06703980, 28.57247260,
-30.13194652, 1.03332063, 24.94855681),
25,3,byrow=TRUE)
if (k == 35) beta = matrix(
c( -3.40189180, 0.92713346, 31.05989534,
-4.52188036, 0.93703071, 32.09872410,
-5.97907586, 0.93890567, 31.96003363,
-5.94712440, 0.97727174, 34.53299133,
-6.29309233, 1.00636112, 36.25124788,
-6.71089295, 1.03283419, 37.75210182,
-8.38691622, 1.02082077, 36.28591385,
-10.43531078, 0.98083830, 33.13256438,
-11.30985554, 0.99454860, 33.50225784,
-12.80509172, 0.97458461, 31.65142746,
-12.96840994, 1.01144058, 33.69945410,
-14.91752468, 0.97258099, 30.50220157,
-15.78042770, 0.97385944, 30.16328051,
-16.23102540, 1.00675003, 31.77616051,
-16.57411667, 1.02867372, 32.92383975,
-17.80722296, 1.00387999, 31.00427739,
-18.56432089, 1.01357688, 31.19720032,
-20.09211544, 0.97796504, 28.39378740,
-21.15486984, 0.97750700, 27.79854046,
-22.02891632, 0.98271510, 27.67808123,
-23.25526587, 0.99321682, 27.51721336,
-24.65449898, 0.94535835, 24.25229057,
-25.87767407, 0.97442736, 25.18649370,
-27.53979094, 0.95282744, 23.20511150,
-30.01082046, 0.91685692, 20.03361673),
25,3,byrow=TRUE)
if (k == 36) beta = matrix(
c( -2.18411218, 0.97764025, 35.24512733,
-3.42768338, 0.98643182, 36.26056059,
-2.88898683, 1.03344700, 40.03169209,
-5.03434617, 1.01504602, 38.19765183,
-7.14143228, 0.98884827, 35.87719583,
-6.44365876, 1.05228443, 40.15835641,
-7.33644084, 1.06273693, 40.47798496,
-7.81222962, 1.09281793, 42.06777372,
-8.62497252, 1.11031113, 42.75113028,
-9.09990075, 1.13092416, 43.82742713,
-10.58004470, 1.12097086, 42.48676913,
-14.26595287, 1.02527598, 34.87158717,
-15.34887785, 1.02626485, 34.32553895,
-16.54588899, 1.02936518, 33.81086542,
-17.21897182, 1.04844837, 34.54260171,
-17.95794773, 1.06766552, 35.27984344,
-19.51533257, 1.03629324, 32.67133541,
-21.06924324, 1.00404695, 29.96124787,
-22.11906531, 0.99724967, 29.08920579,
-23.30316044, 0.99065045, 28.07370235,
-24.13464440, 1.01810829, 29.19048928,
-25.23203250, 1.04075799, 29.87748229,
-26.80940751, 1.01981550, 27.88621124,
-28.70564311, 1.04320299, 28.11622613,
-32.02058598, 1.04570116, 26.33697380),
25,3,byrow=TRUE)
if (k == 37) beta = matrix(
c( 4.96237545, 1.13500821, 49.55454000,
-0.88879878, 1.04122648, 42.12503438,
-2.35069382, 1.03883689, 41.96813093,
-4.46357858, 1.02482957, 40.36943102,
-5.13472407, 1.05482149, 41.97208403,
-6.38471250, 1.05946609, 41.78295272,
-7.85452304, 1.05512345, 40.87328962,
-10.21404555, 1.01870031, 37.53836098,
-11.36819028, 1.01898786, 37.05807620,
-12.54093227, 1.01635998, 36.31816850,
-13.80958526, 1.00364988, 35.00099651,
-15.33641873, 0.99259816, 33.49444177,
-16.15654992, 0.98898087, 32.97912000,
-17.31366457, 0.97321427, 31.54195411,
-18.27791676, 0.96357086, 30.54263397,
-18.79767265, 1.00241461, 32.46396330,
-19.18523508, 1.04936796, 34.96423991,
-19.99538342, 1.06233004, 35.30122987,
-21.37968612, 1.03078730, 32.81051601,
-22.18429164, 1.06323292, 34.24800930,
-23.38539326, 1.05755696, 33.31852137,
-25.29878169, 1.02954167, 30.54026938,
-26.80995112, 1.05544122, 31.16023116,
-28.92403945, 1.02417637, 28.22207761,
-31.77850540, 0.95805763, 22.96722251),
25,3,byrow=TRUE)
if (k == 38) beta = matrix(
c( 1.33123401, 1.04574971, 43.56838471,
-1.02249003, 1.03081935, 42.69352553,
-2.60590890, 1.02960286, 42.46199624,
-5.03386748, 1.00662318, 40.13577025,
-4.84022598, 1.05826122, 43.60195097,
-5.71008884, 1.07393922, 44.31867174,
-4.23324978, 1.14228276, 49.78316782,
-5.43305024, 1.14171630, 49.31508406,
-9.38670501, 1.07417889, 42.83811659,
-12.35863658, 1.01975609, 37.80317367,
-14.76322339, 0.97448773, 33.73800017,
-15.92483383, 0.97857736, 33.31051740,
-16.79956316, 0.98478833, 33.22630913,
-18.35682673, 0.96142387, 31.00877310,
-19.29588663, 0.95928468, 30.40865036,
-20.45545504, 0.93437183, 28.43881209,
-21.45765423, 0.92444520, 27.36609083,
-22.56577441, 0.88706333, 24.70344261,
-23.31772778, 0.92662930, 26.52354799,
-24.27986692, 0.91481091, 25.40327003,
-25.38170576, 0.93972718, 26.17521882,
-26.59632792, 0.92517634, 24.73857869,
-28.01733427, 0.96703695, 26.30494308,
-29.56456700, 0.91612960, 22.70128478,
-32.70868580, 0.93850610, 22.09463252),
25,3,byrow=TRUE)
if (k == 39) beta = matrix(
c( 5.15430037, 1.11132411, 51.04502521,
3.20382719, 1.11505569, 51.51111157,
2.26579400, 1.12976198, 52.75284351,
1.70478095, 1.15960051, 54.81194369,
-0.81045339, 1.14568430, 52.72699034,
-1.09089930, 1.17497088, 54.75851856,
-7.75566411, 1.05526701, 43.23767907,
-8.63732929, 1.06811547, 43.70178295,
-7.28411605, 1.13474373, 49.02252976,
-9.11821730, 1.12306980, 47.24876375,
-10.74836959, 1.11574095, 45.87483121,
-12.43301415, 1.09709216, 43.85072076,
-12.68311992, 1.12345786, 45.48505425,
-14.60913215, 1.10825333, 43.38004215,
-15.59191441, 1.10990426, 42.99786887,
-14.73154944, 1.18937861, 48.64036596,
-16.53048259, 1.16832551, 46.29534543,
-19.45911970, 1.10764914, 40.66886396,
-20.61264100, 1.11904904, 40.73416978,
-22.83687863, 1.07512997, 36.69682239,
-23.63057252, 1.11501763, 38.72599395,
-24.48836498, 1.17656691, 42.01843505,
-26.50792922, 1.18124701, 41.09368797,
-30.20153782, 1.09323998, 33.38471226,
-33.61395119, 1.00206020, 26.05468053),
25,3,byrow=TRUE)
if (k == 40) beta = matrix(
c( -3.35130854, 0.94058360, 36.52606302,
-3.36891886, 0.97357345, 39.86827031,
-4.26561375, 0.98460810, 40.82288701,
-6.54543163, 0.95855119, 38.41130665,
-8.81898894, 0.92581528, 35.46730729,
-10.19461991, 0.92127200, 34.64407264,
-10.90426574, 0.93679164, 35.37145682,
-11.95264669, 0.93808197, 35.02176249,
-12.34848756, 0.96444992, 36.58297963,
-13.59064154, 0.96161791, 35.76037366,
-14.57419256, 0.96936248, 35.72233032,
-14.96507795, 1.01149428, 38.09322964,
-14.17737602, 1.07379663, 42.65854120,
-17.57479064, 0.99973403, 35.92893612,
-18.43607852, 1.01689985, 36.47374756,
-20.28106993, 0.98492061, 33.43948378,
-21.12463625, 1.00251086, 34.04884608,
-21.64987650, 1.05087814, 36.67969240,
-23.45913736, 1.00568101, 32.92837796,
-25.28117062, 0.96363276, 29.29840746,
-26.44477551, 0.98893741, 30.12086854,
-27.54322022, 1.00339074, 30.44677077,
-29.23967429, 0.97820963, 28.00433090,
-31.24787883, 0.98529795, 27.28218372,
-34.24072356, 0.97134889, 24.79985495),
25,3,byrow=TRUE)
beta
}
pv_sup = function(tn,k,l){
if (l<1) tau = l else tau = 1/(1+sqrt(l))
beta = sup_beta(k)
x = as.matrix(beta[,1]+beta[,2]*tn)
x = x*(x>0)
pp = 1-pchisq(x,beta[,3])
taua = (.5-tau+.01)*50
tau1 = floor(taua)
p = (tau1+1-taua)*pp[tau1] + (taua-tau1)*pp[tau1+1]
if (tau == .5) p = 1- pchisq(tn,k)
if (tau <= .01) p = pp[25]
if (tau >= .49) p = ((.5-tau)*pp[1]+(tau-.49)*(1-pchisq(tn,k)))*100
p
}
####################################################################
#***************** End of Hansens function ************************#
####################################################################
if (!inherits(mod, "formula")) { # Wenn Modell übergeben ...
mf = model.frame(mod)
X = model.matrix(terms(mod), mf)
y = model.response(model.frame(mod))
}
else { # Wenn Formel übergeben ...
mf = model.frame(mod, data = data)
y = model.response(mf)
X = model.matrix(mod, data = data)
}
n = nrow(X) # Number of observations
k = ncol(X) # Number of coefs
# Residuals
SSR = sum((lm.fit(X, y)$residuals)^2)
# Some pre-calculations
pot = from:to # Define points of time to be analyzed
npot = length(pot) # How many points of time?
chi2.stats = rep(0, npot) # Initialize vector of f.stats
k = ncol(X) # Number of parameters
tAll = length(y) # Sample sisze
if ((from < round(0.15 * tAll)) | (to > round(0.85 * tAll))) warning("Specified range is too close to borders of dataset. Test statistic looses asymptotic properties and qlr-test will be unreliable!")
if (to+1 >= tAll) stop("Specified range must end at least two periods before data set ends.")
for (i in 1:npot) {
X1 = as.matrix(X[(1:pot[i]), ])
X2 = as.matrix(X[((pot[i] + 1):tAll), ])
fit1 = lm.fit(X1, y[1:pot[i]])
fit2 = lm.fit(X2, y[((pot[i] + 1):tAll)])
u = c(fit1$residuals, fit2$residuals)
sigma2 = (sum(u^2))/(tAll - 2 * k)
chi2.stats[i] = (SSR - sum(u^2))/sigma2
}
chi2.stats = t(as.matrix(chi2.stats))
dimnames(chi2.stats) = list("", pot)
max.point = which.max(chi2.stats) + from - 1
chi2.val = max(chi2.stats)
f.stats = chi2.stats/k
f.val = chi2.val/k
cv = qlr.cv(tAll, from, to, k, sig.level)
f.crit = cv$cv.f[,2]
p.value = pv_sup(chi2.val, k, cv$lambda)
H = c(paste("No break in t = ", from,"...",to, sep = ""), paste("Some break in t = ", from,"...",to, sep = ""))
names(H) = c("H0:", "H1:")
H = t(H)
test.result = if (f.val > max(f.crit)) "rej."
else if (f.val < min(f.crit)) "not rej."
else if (f.val >= min(f.crit) & f.val <= max(f.crit)) "ambiguous, use p.value!"
results = data.frame(f.value = f.val,
lower.cv = f.crit[1],
upper.cv = f.crit[2],
p.value = p.value,
sig.level = sig.level,
H0 = test.result,
row.names = "")
out = list()
attr(out, "title") = "QLR-Test for structural breaks at unknown date"
out$hyp = H # Null and alternative hypothesis
out$results = results # Basic test results
out$chi2.stats = chi2.stats
out$f.stats = f.stats
out$f.crit = f.crit
out$p.value = p.value
out$breakpoint = max.point
out$periods = pot
out$lf.crit = cv$cv.f
out$lambda = cv$lambda
attr(out, "two.sided") = T
attr(out, "details") = if (details) {T} else {F}
attr(out, "type") = "htest"
attr(out, "test.type") = "qlrtest"
class(out) = c("desk")
return(out)
}
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