R/Reimann.R

In FGN: Fractional Gaussian Noise and power law decay time series model fitting

Reimann <-
function (v) {
stopifnot(v>=0, v<=3)
z <-
c(0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 
0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 
0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 
0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 
0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 
0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 
0.66, 0.67, 0.68, 0.69, 0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 
0.77, 0.78, 0.79, 0.8, 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87, 
0.88, 0.89, 0.9, 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98, 
0.99, 0.999, 0.9999, 1.0001, 1.001, 1.01, 1.02, 1.03, 1.04, 1.05, 
1.06, 1.07, 1.08, 1.09, 1.1, 1.11, 1.12, 1.13, 1.14, 1.15, 1.16, 
1.17, 1.18, 1.19, 1.2, 1.21, 1.22, 1.23, 1.24, 1.25, 1.26, 1.27, 
1.28, 1.29, 1.3, 1.31, 1.32, 1.33, 1.34, 1.35, 1.36, 1.37, 1.38, 
1.39, 1.4, 1.41, 1.42, 1.43, 1.44, 1.45, 1.46, 1.47, 1.48, 1.49, 
1.5, 1.51, 1.52, 1.53, 1.54, 1.55, 1.56, 1.57, 1.58, 1.59, 1.6, 
1.61, 1.62, 1.63, 1.64, 1.65, 1.66, 1.67, 1.68, 1.69, 1.7, 1.71, 
1.72, 1.73, 1.74, 1.75, 1.76, 1.77, 1.78, 1.79, 1.8, 1.81, 1.82, 
1.83, 1.84, 1.85, 1.86, 1.87, 1.88, 1.89, 1.9, 1.91, 1.92, 1.93, 
1.94, 1.95, 1.96, 1.97, 1.98, 1.99, 2, 2.01, 2.02, 2.03, 2.04, 
2.05, 2.06, 2.07, 2.08, 2.09, 2.1, 2.11, 2.12, 2.13, 2.14, 2.15, 
2.16, 2.17, 2.18, 2.19, 2.2, 2.21, 2.22, 2.23, 2.24, 2.25, 2.26, 
2.27, 2.28, 2.29, 2.3, 2.31, 2.32, 2.33, 2.34, 2.35, 2.36, 2.37, 
2.38, 2.39, 2.4, 2.41, 2.42, 2.43, 2.44, 2.45, 2.46, 2.47, 2.48, 
2.49, 2.5, 2.51, 2.52, 2.53, 2.54, 2.55, 2.56, 2.57, 2.58, 2.59, 
2.6, 2.61, 2.62, 2.63, 2.64, 2.65, 2.66, 2.67, 2.68, 2.69, 2.7, 
2.71, 2.72, 2.73, 2.74, 2.75, 2.76, 2.77, 2.78, 2.79, 2.8, 2.81, 
2.82, 2.83, 2.84, 2.85, 2.86, 2.87, 2.88, 2.89, 2.9, 2.91, 2.92, 
2.93, 2.94, 2.95, 2.96, 2.97, 2.98, 2.99, 3)
f <-
c(-0.5, -0.50929071403984, -0.518788211482836, -0.52849887255538, 
-0.53842934310324, -0.548586548573048, -0.558977708886255, -0.569610354272701, 
-0.580492342136792, -0.591631875035709, -0.603037519856238, -0.614718228284357, 
-0.626683358670459, -0.638942699402589, -0.651506493910323, -0.664385467433628, 
-0.67759085570376, -0.691134435697607, -0.70502855864212, -0.719286185463725, 
-0.733920924896338, -0.748947074483669, -0.764379664735542, -0.780234506725018, 
-0.796528243443113, -0.813278405261886, -0.830503469894669, -0.848222927284306, 
-0.86645734989895, -0.885228468968234, -0.904559257253985, -0.924474019018421, 
-0.94499848793068, -0.9661599337411, -0.987987278653202, -1.01051122443759, 
-1.03376439146293, -1.05778147096781, -1.08259939206872, -1.10825750519494, 
-1.13479778386698, -1.16226504699479, -1.19070720417243, -1.22017552679311, 
-1.25072494821236, -1.2824143966562, -1.31530716511919, -1.34947132313758, 
-1.3849801760749, -1.42191277844102, -1.46035450880959, -1.50039771513341, 
-1.54214244072436, -1.58569724291148, -1.63118011848059, -1.67871955250588, 
-1.72845571020389, -1.78054179509282, -1.83514560117446, -1.89245129226477, 
-1.952661448224, -2.01599942599146, -2.0827120934152, -2.15307300640549, 
-2.22738611561378, -2.30599010854238, -2.38926351790878, -2.47763075880344, 
-2.5715692978147, -2.67161820972618, -2.7783884455537, -2.89257522500358, 
-3.01497308445774, -3.14649426895547, -3.28819136847861, -3.44128538694522, 
-3.60720082845166, -3.7876099364473, -3.98448899813876, -4.20019073586667, 
-4.43753841589555, -4.69994967576882, -4.9916016274488, -5.31765423215314, 
-5.68455744075495, -6.1004811903429, -6.5759296850213, -7.12463919092564, 
-7.76492472874585, -8.52176132580756, -9.43011401940225, -10.5404878623373, 
-11.9286404326486, -13.7136193516382, -16.0938373199491, -19.4264371969308, 
-24.4257046990521, -32.7583064951388, -49.4242425873268, -99.4235129777281, 
-999.422857155788, -Inf, Inf, 1000.57728847601, 100.577943338497, 
50.5786700410156, 33.912729103772, 25.5801205247701, 20.580844302037, 
17.248233766956, 14.8680032033142, 13.0830097520643, 11.6948407129121, 
10.5844484649508, 9.67607543058626, 8.91921655749934, 8.2789068089333, 
7.73017115814363, 7.25469458506812, 6.83874082424536, 6.4718056722916, 
6.14571919288521, 5.85403143596652, 5.59158244117775, 5.35419509746289, 
5.13845176823124, 4.94152918821738, 4.76107463612619, 4.59511182584294, 
4.44196851505651, 4.30022020085516, 4.16864588055177, 4.04619296544179, 
3.93194921180954, 3.82512008464303, 3.72501036565211, 3.63100910528344, 
3.54257723026215, 3.45923727555487, 3.38056482767235, 3.30618135554451, 
3.23574817336266, 3.16896133221512, 3.10554727797758, 3.04525914463405, 
2.98787357712343, 2.93318799750975, 2.88101824394744, 2.83119652445112, 
2.78356963756506, 2.73799742018119, 2.69435138937978, 2.65251355057544, 
2.61237534868549, 2.57383674269036, 2.5368053869754, 2.50119590535102, 
2.46692924573723, 2.43393210524621, 2.40213641686317, 2.37147889016082, 
2.3419005995261, 2.31334661426216, 2.28576566568013, 2.25910984693594, 
2.23333434191523, 2.20839717993866, 2.18425901346369, 2.16088291630605, 
2.13823420020486, 2.11628024781464, 2.09499036043334, 2.07433561897139, 
2.05428875683775, 2.03482404356788, 2.01591717814942, 1.99754519111563, 
1.97968635457718, 1.96232009945134, 1.94542693922581, 1.92898839966291, 
1.9129869539112, 1.89740596254533, 1.88222961810282, 1.86744289372935, 
1.85303149558155, 1.83898181867069, 1.82528090586028, 1.81191640975802, 
1.79887655726642, 1.78615011657815, 1.77372636642181, 1.76159506738094, 
1.74974643512506, 1.73817111540579, 1.72686016068356, 1.71580500826231, 
1.70499745981986, 1.69442966223105, 1.68409408958945, 1.67398352634113, 
1.66409105145104, 1.65441002352903, 1.64493406684823, 1.63565705819409, 
1.626573114487, 1.61767658112584, 1.60896202100411, 1.60042420415364, 
1.59205809797453, 1.58385885801291, 1.57582181925111, 1.56794248787718, 
1.56021653350336, 1.55263978180527, 1.54520820755524, 1.53791792802575, 
1.53076519673988, 1.52374639754793, 1.51685803901038, 1.51009674906889, 
1.50345926998828, 1.49694245355352, 1.49054325650689, 1.48425873621135, 
1.47808604652723, 1.47202243389, 1.46606523357791, 1.46021186615865, 
1.45445983410535, 1.44880671857234, 1.44325017632213, 1.43778793679524, 
1.43241779931532, 1.42713763042226, 1.4219453613265, 1.41683898547822, 
1.41181655624534, 1.4068761846947, 1.40201603747119, 1.39723433476967, 
1.39252934839517, 1.3878993999067, 1.38334285884074, 1.37885814101019, 
1.37444370687532, 1.37009805998295, 1.36581974547074, 1.36160734863336, 
1.35745949354753, 1.35337484175327, 1.34935209098849, 1.34538997397465, 
1.34148725725092, 1.33764274005466, 1.33385525324615, 1.33012365827543, 
1.32644684618938, 1.32282373667729, 1.3192532771531, 1.31573444187269, 
1.31226623108474, 1.30884767021359, 1.30547780907278, 1.30215572110782, 
1.29888050266709, 1.29565127229955, 1.29246717007809, 1.28932735694755, 
1.28623101409629, 1.28317734235029, 1.28016556158894, 1.27719491018153, 
1.27426464444368, 1.27137403811277, 1.26852238184172, 1.26570898271029, 
1.26293316375328, 1.26019426350483, 1.25749163555832, 1.25482464814114, 
1.25219268370383, 1.24959513852296, 1.24703142231725, 1.24450095787645, 
1.24200318070237, 1.23953753866178, 1.23710349165055, 1.2347005112687, 
1.23232808050597, 1.22998569343741, 1.22767285492874, 1.22538908035102, 
1.22313389530436, 1.22090683535029, 1.2187074457525, 1.21653528122565, 
1.2143899056919, 1.21227089204498, 1.21017782192145, 1.20811028547897, 
1.20606788118121, 1.20405021558931, 1.20205690315959)
approx(z, f, xout=v)$y
}