arx.ls: The ARX estimation by OLS function

In MARX: Simulation, Estimation, Model Selection and Forecasting for MARX Models

Description

This function allows you to estimate ARX models by ordinary least squares (OLS).

Usage

arx.ls(y, x, p)

Arguments

y	Data vector of time series observations.
x	Matrix of data (every column represents one time series). Specify NULL or "not" if not wanted.
p	Number of autoregressive terms to be included.

Value

coefficients	Vector of estimated coefficients.
coef.auto	Vector of estimated autoregressive parameters.
coef.exo	Vector of estimated exogenous parameters.
mse	Mean squared error.
residuals	Residuals.
loglikelihood	Value of the loglikelihood.
fitted.values	Fitted values.
df	Degrees of freedom.
vcov	Variance-covariance matrix of residuals.

Author(s)

Sean Telg

Examples

data <- sim.marx(c('t',3,1),c('t',1,1),100,0.5,0.4,0.3)
arx.ls(data$y,data$x,2)

Example output

$coefficients
             [,1]
int   -0.16545633
lag 1  0.69757873
lag 2 -0.08328851
exo 1  0.28296525

$coef.auto
[1]  0.69757873 -0.08328851

$coef.exo
[1] 0.2829652

$mse
[1] 9.482181

$residuals
              [,1]
 [1,]   2.78749361
 [2,]  -0.61250441
 [3,]  -0.17108762
 [4,]  -2.52609408
 [5,]  -4.30936370
 [6,]  -6.22955804
 [7,]   2.63919562
 [8,]   7.02735802
 [9,]   5.30196661
[10,]  -2.05201495
[11,]  -3.24579121
[12,]  -0.14825471
[13,]  -0.38052357
[14,]   5.10462152
[15,]  11.13586609
[16,]  -2.22675195
[17,]  -0.90968257
[18,]   2.88186614
[19,]   5.09829320
[20,]  -0.84198019
[21,]   0.05726359
[22,]   0.65278135
[23,]  -0.94535460
[24,]   0.62080654
[25,]  -2.20418047
[26,]   1.78495575
[27,]   0.29625782
[28,]  -0.69793860
[29,]  -0.91342965
[30,]   0.39194661
[31,]  -0.31735917
[32,]   0.45583202
[33,]   0.99852106
[34,]  -0.69633104
[35,]   2.12535273
[36,]   1.26932342
[37,]   1.70892063
[38,]   0.08605043
[39,]   1.44553126
[40,]   0.49699790
[41,]   1.05869107
[42,]   4.92701273
[43,]  -1.48747586
[44,]  -2.59635194
[45,]  -1.00537399
[46,]  -0.71234351
[47,]  -1.06702246
[48,]  -0.17702215
[49,]  -2.25457580
[50,]   1.27729409
[51,]   1.61310143
[52,]   2.66597979
[53,]   0.71981226
[54,]  -2.54856777
[55,]  -2.11558539
[56,]   1.87139103
[57,]   1.85909054
[58,]  -1.04024854
[59,]   0.33627482
[60,]   0.13109445
[61,]  -0.33858825
[62,]   1.58896812
[63,]   0.39868286
[64,]  -1.59790486
[65,]   0.98979540
[66,]   0.61924292
[67,]   2.20895498
[68,]   0.35749701
[69,]  -2.03723980
[70,]   0.28419764
[71,]   0.74996734
[72,]   0.03448765
[73,]   0.13266915
[74,]   5.63102458
[75,]  -1.30406527
[76,]   1.21816808
[77,]   0.61600781
[78,]   0.96347170
[79,]   0.18275442
[80,]   1.57276544
[81,]  -3.09153725
[82,]  -4.81771608
[83,]  -5.81960327
[84,] -16.51887704
[85,]  -5.57110819
[86,]   3.84327299
[87,]  -0.11635135
[88,]  -0.61434054
[89,]  -3.43093877
[90,]  -2.68552199
[91,]  -0.55257775
[92,]  -1.23261654
[93,]   0.12277729
[94,]   0.16748681
[95,]  -1.81840239
[96,]   0.90608698
[97,]   1.63656921
[98,]   0.92836475

$loglikelihood
[1] -249.2773

$fitted.values
               [,1]
 [1,]   0.125048508
 [2,]   4.181753574
 [3,]   1.790375945
 [4,]   1.024369981
 [5,]  -1.065586670
 [6,]  -3.886566500
 [7,] -22.819141211
 [8,] -13.289572854
 [9,]  -2.042343656
[10,]  13.745940610
[11,]   4.827001199
[12,]  -0.346172924
[13,]  -0.640205532
[14,]  -3.468043623
[15,]   1.840269827
[16,]   8.879157607
[17,]   3.052166768
[18,]   1.311956017
[19,]   2.621315612
[20,]   4.287637366
[21,]   1.530863664
[22,]   2.406520567
[23,]   2.713344814
[24,]   0.729813724
[25,]  -3.246706718
[26,]  -4.227226950
[27,]  -1.355318202
[28,]  -0.233471860
[29,]  -0.899672775
[30,]  -1.860354144
[31,]  -1.611776394
[32,]  -1.406665001
[33,]  -0.531383417
[34,]  -0.535239479
[35,]  -0.086144804
[36,]   1.436088729
[37,]   2.369571328
[38,]   1.603662144
[39,]   0.542828063
[40,]   1.146670466
[41,]   1.034038531
[42,]   0.253728751
[43,]  15.637995467
[44,]   8.733898224
[45,]   3.384756711
[46,]  -0.539742461
[47,]  -0.949318932
[48,]  -1.510335147
[49,]  -1.135167869
[50,]  -2.365531774
[51,]  -0.406303379
[52,]   1.281424964
[53,]   3.912413188
[54,]   2.572326647
[55,]  -0.807066252
[56,]  -1.839490513
[57,]   0.153362774
[58,]   3.122979613
[59,]   1.473713082
[60,]   1.777329538
[61,]  -0.907425621
[62,]  -1.463920113
[63,]   0.002091177
[64,]  -0.468253225
[65,]  -1.417337600
[66,]  -0.406657626
[67,]   0.080058702
[68,]   0.613114873
[69,]  -1.348425270
[70,]  -4.779661201
[71,]  -2.996029989
[72,]  -2.032038612
[73,]  -1.651567653
[74,]  -1.646824755
[75,]   2.427465453
[76,]   0.007965706
[77,]   0.378073848
[78,]   0.079878164
[79,]  -0.748836768
[80,]  -1.282983657
[81,]   1.618291758
[82,]  -1.256211400
[83,]  -4.357379205
[84,]  -5.275875394
[85,] -38.811598088
[86,] -39.867245973
[87,] -22.124698883
[88,] -16.969287388
[89,] -10.242262101
[90,]  -8.152136513
[91,]  -7.339013039
[92,]  -5.025123548
[93,]  -6.920913365
[94,]  -3.978477164
[95,]  -2.035133454
[96,]  -3.287471099
[97,]  -1.561187015
[98,]  -0.172151765

$df
[1] 94

$vcov
             int                                          
int 0.1056840524  0.0006154339  0.0017199291  0.0006222327
    0.0006154339  0.0060998978 -0.0046815830 -0.0010553121
    0.0017199291 -0.0046815830  0.0051708760  0.0006078471
    0.0006222327 -0.0010553121  0.0006078471  0.0008073077

MARX documentation built on May 2, 2019, 3:42 a.m.