# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
library(readxl)
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library(lubridate)
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library(tidyverse)
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library(car)
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library(tseries)
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library(astsa)
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library(foreign)
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library(timsac)
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library(vars)
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library(lmtest)
library(mFilter)
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library(dynlm)
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library(nlme)
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library(broom)
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library(kableExtra)
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library(knitr)
library(MASS)
library(parallel)
library(car)
library(mlogit)
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library(tidyr)
library(forecast)
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library(fpp2)
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library(stats)
library(quantmod)
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## first, last
## Loading required package: TTR
library(urca)
library(xts)
varinfla <- read_excel("E:/SERIES DE TIEMPO/TAREA 09/varinfla.xls")
#View(varinfla)
attach(varinfla)
names(varinfla)
## [1] "M2" "INPC"
#Generar Serie de Tiempo para Oferta M2
tm2 <- ts(varinfla[,1], start = c(2000,1),frequency = 12)
#Generar Serie de Tiempo para INPC
tp <- ts(varinfla[,2], start = c(2000,1),frequency = 12)
#Generar Logaritmos para las variables
# Para M2
ltm2 <- log(tm2)
ndiffs(ltm2)
## [1] 2
#Para INPC
ltp <- log(tp)
ndiffs(ltp)
## [1] 1
#Para Graficar
par(mfrow=c(2,1), mar=c(2,2,2,1)+.1)
ts.plot(ltp, ltm2, col = c("blue","red"))
#Probar la Estacionariedad
#Primera Diferencia de Log del Indice de Precio
dltp <- diff(ltp)
#Segunda Diferencia de Log del Indice de Precio
d2ltp <- diff(dltp)
#Primera Diferencia de Log del Oferta de Dinero M2
dltm2 <- diff(ltm2)
#Segunda Diferencia de Log del Oferta de Dinero M2
d2ltm2 <- diff(dltm2)
#Para Graficar
par(mfrow=c(2,1), mar=c(2,2,2,1)+.1)
ts.plot(d2ltp,d2ltm2, col = c("blue","red"))
#Pruebas de Causalidad de Granger
grangertest(d2ltp~d2ltm2, order(1))
## Granger causality test
##
## Model 1: d2ltp ~ Lags(d2ltp, 1:1) + Lags(d2ltm2, 1:1)
## Model 2: d2ltp ~ Lags(d2ltp, 1:1)
## Res.Df Df F Pr(>F)
## 1 170
## 2 171 -1 0.8796 0.3496
#A prueba y error
grangertest(d2ltp~d2ltm2, order = 4)
## Granger causality test
##
## Model 1: d2ltp ~ Lags(d2ltp, 1:4) + Lags(d2ltm2, 1:4)
## Model 2: d2ltp ~ Lags(d2ltp, 1:4)
## Res.Df Df F Pr(>F)
## 1 161
## 2 165 -4 2.7105 0.03202 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
grangertest(d2ltm2~d2ltp, order=1)
## Granger causality test
##
## Model 1: d2ltm2 ~ Lags(d2ltm2, 1:1) + Lags(d2ltp, 1:1)
## Model 2: d2ltm2 ~ Lags(d2ltm2, 1:1)
## Res.Df Df F Pr(>F)
## 1 170
## 2 171 -1 0.0909 0.7634
#Nunca acepta que INPC causa a M2
grangertest(d2ltm2~d2ltp, order=12)
## Granger causality test
##
## Model 1: d2ltm2 ~ Lags(d2ltm2, 1:12) + Lags(d2ltp, 1:12)
## Model 2: d2ltm2 ~ Lags(d2ltm2, 1:12)
## Res.Df Df F Pr(>F)
## 1 137
## 2 149 -12 1.0124 0.441
#Crear nuevo Objeto para VAR
vard2ltm2 <- ts(d2ltm2, start = 2000, frequency = 12)
vard2ltp <- ts(d2ltp, start = 2000, frequency = 12)
ejvar <- (cbind(vard2ltm2,vard2ltp))
print(ejvar)
## vard2ltm2 vard2ltp
## Jan 2000 -0.0009656447 -3.300864e-03
## Feb 2000 -0.0064430432 1.433194e-04
## Mar 2000 -0.0022454019 -1.942120e-03
## Apr 2000 0.0072742598 2.174874e-03
## May 2000 0.0064035137 -2.013323e-03
## Jun 2000 -0.0201644392 1.586132e-03
## Jul 2000 0.0099649039 1.799609e-03
## Aug 2000 -0.0150664921 -4.155866e-04
## Sep 2000 0.0158047270 1.650813e-03
## Oct 2000 -0.0059265096 2.254195e-03
## Nov 2000 -0.0088730913 -5.239221e-03
## Dec 2000 0.0314569386 -6.190872e-03
## Jan 2001 -0.0149667317 6.977952e-03
## Feb 2001 -0.0032927813 -1.284381e-03
## Mar 2001 -0.0057350086 -2.738878e-03
## Apr 2001 0.0047653308 6.938669e-05
## May 2001 0.0014831800 -4.963577e-03
## Jun 2001 0.0145958761 8.508847e-03
## Jul 2001 -0.0142772414 3.359543e-03
## Aug 2001 -0.0020401552 -4.757453e-03
## Sep 2001 0.0102406429 -7.493690e-04
## Oct 2001 -0.0119120420 -2.376678e-03
## Nov 2001 -0.0168888485 7.805078e-03
## Dec 2001 0.0217069284 -9.830555e-03
## Jan 2002 0.0050543500 5.743571e-03
## Feb 2002 -0.0108292217 3.468257e-04
## Mar 2002 -0.0010265422 -3.423306e-03
## Apr 2002 0.0065279437 2.838752e-03
## May 2002 -0.0041124272 -1.996990e-03
## Jun 2002 -0.0083273029 9.279053e-04
## Jul 2002 0.0035996601 2.203648e-03
## Aug 2002 0.0024811310 -1.601151e-03
## Sep 2002 0.0045389594 3.658899e-03
## Oct 2002 0.0096318710 -3.713197e-03
## Nov 2002 -0.0159336405 -3.078636e-04
## Dec 2002 0.0076303038 -1.261123e-03
## Jan 2003 -0.0018470875 3.518818e-03
## Feb 2003 -0.0125354435 -4.587421e-03
## Mar 2003 0.0205292106 -4.937218e-03
## Apr 2003 -0.0123601637 4.059175e-03
## May 2003 0.0082810134 6.207614e-04
## Jun 2003 -0.0147877468 1.546898e-03
## Jul 2003 0.0099141118 2.940433e-03
## Aug 2003 -0.0004298882 -2.275070e-03
## Sep 2003 0.0095211657 4.606121e-03
## Oct 2003 0.0078812381 -3.976974e-03
## Nov 2003 -0.0345416385 1.906965e-03
## Dec 2003 0.0092926219 -2.322832e-04
## Jan 2004 0.0232625468 -2.580838e-03
## Feb 2004 -0.0233207029 -1.875028e-03
## Mar 2004 0.0030061446 -4.020139e-03
## Apr 2004 0.0119419398 4.113677e-03
## May 2004 -0.0154335193 1.015504e-03
## Jun 2004 0.0001925633 3.537022e-03
## Jul 2004 0.0116919246 2.080755e-03
## Aug 2004 -0.0003235563 -1.333408e-03
## Sep 2004 -0.0039087062 1.592438e-03
## Oct 2004 0.0150296349 -6.430308e-03
## Nov 2004 -0.0169129832 -2.027544e-03
## Dec 2004 0.0008938633 3.290152e-03
## Jan 2005 0.0140946961 1.170862e-03
## Feb 2005 -0.0212348273 -9.419461e-04
## Mar 2005 0.0151762071 -6.070256e-03
## Apr 2005 0.0005392421 1.554334e-03
## May 2005 -0.0104422142 4.867123e-03
## Jun 2005 0.0031031862 -2.712739e-03
## Jul 2005 0.0025801935 2.805645e-03
## Aug 2005 0.0043022503 -1.547461e-03
## Sep 2005 -0.0020854570 4.719695e-03
## Oct 2005 -0.0065375363 -1.048068e-03
## Nov 2005 0.0021215328 -2.764838e-04
## Dec 2005 0.0047121568 -4.318427e-03
## Jan 2006 -0.0021305229 -2.742516e-04
## Feb 2006 -0.0070880590 2.107601e-04
## Mar 2006 -0.0133381185 -5.926028e-03
## Apr 2006 0.0254550678 5.323591e-03
## May 2006 -0.0144913343 1.876376e-03
## Jun 2006 -0.0040488707 2.350334e-03
## Jul 2006 0.0138230404 4.955049e-03
## Aug 2006 -0.0077958419 -5.681694e-03
## Sep 2006 0.0170086392 8.709111e-04
## Oct 2006 0.0095222854 5.337172e-04
## Nov 2006 -0.0324840149 -6.158620e-04
## Dec 2006 0.0094367374 -2.359720e-03
## Jan 2007 -0.0006788772 -6.303641e-04
## Feb 2007 -0.0131973740 -2.758192e-03
## Mar 2007 0.0216596393 -4.293509e-03
## Apr 2007 -0.0067165994 6.090790e-03
## May 2007 0.0010056133 3.037773e-03
## Jun 2007 0.0003685911 -1.726515e-04
## Jul 2007 -0.0032425089 3.669315e-03
## Aug 2007 -0.0039171221 -3.845367e-03
## Sep 2007 0.0138264544 3.140722e-03
## Oct 2007 -0.0038356531 -2.904514e-03
## Nov 2007 -0.0048027366 4.981865e-04
## Dec 2007 -0.0034446193 -1.655513e-03
## Jan 2008 0.0041665137 4.253795e-03
## Feb 2008 -0.0043215314 -4.948926e-03
## Mar 2008 0.0037637710 -3.354650e-03
## Apr 2008 -0.0138527844 5.211072e-03
## May 2008 0.0125473452 1.428201e-03
## Jun 2008 -0.0030381451 1.998493e-04
## Jul 2008 0.0124337100 1.034705e-03
## Aug 2008 -0.0008792738 -1.663343e-06
## Sep 2008 0.0062059713 4.512291e-03
## Oct 2008 0.0346517958 -4.401623e-03
## Nov 2008 -0.0474924494 -4.586251e-03
## Dec 2008 -0.0160262067 -1.100275e-04
## Jan 2009 0.0143375679 3.530679e-03
## Feb 2009 -0.0022555799 -2.241614e-03
## Mar 2009 -0.0046845933 -6.411269e-03
## Apr 2009 0.0009379857 4.756749e-03
## May 2009 0.0072088651 8.809519e-04
## Jun 2009 -0.0094252829 -3.310929e-04
## Jul 2009 0.0072476740 2.614121e-03
## Aug 2009 0.0056404973 -1.982801e-03
## Sep 2009 -0.0048856272 2.153140e-03
## Oct 2009 -0.0005313973 -1.043522e-03
## Nov 2009 -0.0089354641 6.680997e-03
## Dec 2009 0.0066777336 -5.044067e-03
## Jan 2010 0.0057734358 1.305947e-03
## Feb 2010 -0.0126999675 -1.026479e-02
## Mar 2010 0.0159985950 -3.129268e-03
## Apr 2010 -0.0040113168 6.007953e-03
## May 2010 0.0071575871 2.481411e-03
## Jun 2010 -0.0082967966 6.046531e-04
## Jul 2010 0.0003263858 2.455062e-03
## Aug 2010 -0.0084801335 9.259169e-04
## Sep 2010 -0.0009986335 1.826049e-03
## Oct 2010 0.0080032082 -3.038436e-03
## Nov 2010 -0.0026087628 -8.216876e-05
## Dec 2010 0.0011224692 -1.115309e-03
## Jan 2011 0.0010306492 -1.827853e-03
## Feb 2011 -0.0010353560 -1.995946e-03
## Mar 2011 -0.0005180177 -7.319772e-03
## Apr 2011 0.0037881254 7.349164e-03
## May 2011 0.0032352507 4.836537e-03
## Jun 2011 0.0034178950 -3.206050e-03
## Jul 2011 0.0060473346 8.698036e-04
## Aug 2011 -0.0157200082 4.274476e-03
## Sep 2011 0.0026226442 4.033213e-03
## Oct 2011 0.0014988951 -2.574031e-03
## Nov 2011 -0.0013007220 -1.130269e-03
## Dec 2011 -0.0039180629 -5.022855e-03
## Jan 2012 0.0041655904 -1.456827e-03
## Feb 2012 -0.0050358383 -3.716026e-03
## Mar 2012 0.0108550818 -1.952801e-05
## Apr 2012 -0.0042922230 7.761186e-03
## May 2012 0.0010784426 9.988571e-04
## Jun 2012 -0.0093059519 -2.601974e-03
## Jul 2012 -0.0018778205 1.401118e-03
## Aug 2012 0.0063698251 6.490278e-04
## Sep 2012 0.0069633209 1.723851e-03
## Oct 2012 -0.0165391660 -4.474105e-03
## Nov 2012 0.0063414395 1.723604e-03
## Dec 2012 0.0014308158 8.899776e-04
## Jan 2013 -0.0006560887 2.400921e-03
## Feb 2013 -0.0017996569 -6.650610e-03
## Mar 2013 0.0030126978 -3.993886e-03
## Apr 2013 -0.0015516428 2.726267e-03
## May 2013 0.0049329896 2.758893e-04
## Jun 2013 0.0017991528 3.172438e-03
## Jul 2013 0.0006590120 9.162040e-04
## Aug 2013 0.0007355575 9.878215e-04
## Sep 2013 0.0013661606 4.533737e-03
## Oct 2013 -0.0146513136 -3.558836e-03
## Nov 2013 0.0120330086 3.181373e-03
## Dec 2013 -0.0031824817 -6.371310e-03
## Jan 2014 0.0004630717 2.058411e-04
## Feb 2014 0.0052105665 -4.603223e-03
## Mar 2014 -0.0058410488 -1.335619e-03
## Apr 2014 -0.0038726265 4.934402e-03
## May 2014 0.0056098149 1.014936e-03
## Jun 2014 -0.0006490686 8.391137e-04
#Proceso VAR
library(vars)
VARselect(diff(ejvar),lag.max=10,type="const")
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 9 8 4 9
##
## $criteria
## 1 2 3 4 5
## AIC(n) -1.898702e+01 -1.963128e+01 -1.979002e+01 -2.003526e+01 -2.006519e+01
## HQ(n) -1.894079e+01 -1.955422e+01 -1.968214e+01 -1.989655e+01 -1.989566e+01
## SC(n) -1.887314e+01 -1.944148e+01 -1.952430e+01 -1.969361e+01 -1.964763e+01
## FPE(n) 5.676016e-09 2.980308e-09 2.543027e-09 1.990199e-09 1.931867e-09
## 6 7 8 9 10
## AIC(n) -2.017471e+01 -2.022228e+01 -2.032575e+01 -2.034096e+01 -2.031853e+01
## HQ(n) -1.997437e+01 -1.999111e+01 -2.006375e+01 -2.004814e+01 -1.999489e+01
## SC(n) -1.968123e+01 -1.965288e+01 -1.968042e+01 -1.961971e+01 -1.952137e+01
## FPE(n) 1.731920e-09 1.652069e-09 1.490397e-09 1.468790e-09 1.503231e-09
VARselect(ejvar, lag.max =12)
## $selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 11 11 2 11
##
## $criteria
## 1 2 3 4 5
## AIC(n) -2.046463e+01 -2.068196e+01 -2.065764e+01 -2.075149e+01 -2.075348e+01
## HQ(n) -2.041820e+01 -2.060458e+01 -2.054931e+01 -2.061220e+01 -2.058323e+01
## SC(n) -2.035027e+01 -2.049137e+01 -2.039081e+01 -2.040842e+01 -2.033417e+01
## FPE(n) 1.295173e-09 1.042211e-09 1.067940e-09 9.723977e-10 9.706467e-10
## 6 7 8 9 10
## AIC(n) -2.090388e+01 -2.097478e+01 -2.104458e+01 -2.103653e+01 -2.109132e+01
## HQ(n) -2.070268e+01 -2.074263e+01 -2.078147e+01 -2.074247e+01 -2.076631e+01
## SC(n) -2.040834e+01 -2.040300e+01 -2.039656e+01 -2.031228e+01 -2.029083e+01
## FPE(n) 8.353390e-10 7.784502e-10 7.263246e-10 7.326459e-10 6.941160e-10
## 11 12
## AIC(n) -2.130916e+01 -2.130390e+01
## HQ(n) -2.095320e+01 -2.091699e+01
## SC(n) -2.043244e+01 -2.035094e+01
## FPE(n) 5.587598e-10 5.623294e-10
var1 <- VAR(ejvar,p=11)
var1
##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation vard2ltm2:
## ==============================================
## Call:
## vard2ltm2 = vard2ltm2.l1 + vard2ltp.l1 + vard2ltm2.l2 + vard2ltp.l2 + vard2ltm2.l3 + vard2ltp.l3 + vard2ltm2.l4 + vard2ltp.l4 + vard2ltm2.l5 + vard2ltp.l5 + vard2ltm2.l6 + vard2ltp.l6 + vard2ltm2.l7 + vard2ltp.l7 + vard2ltm2.l8 + vard2ltp.l8 + vard2ltm2.l9 + vard2ltp.l9 + vard2ltm2.l10 + vard2ltp.l10 + vard2ltm2.l11 + vard2ltp.l11 + const
##
## vard2ltm2.l1 vard2ltp.l1 vard2ltm2.l2 vard2ltp.l2 vard2ltm2.l3
## -7.629557e-01 -1.714432e-01 -8.434147e-01 1.109554e-01 -6.063436e-01
## vard2ltp.l3 vard2ltm2.l4 vard2ltp.l4 vard2ltm2.l5 vard2ltp.l5
## -6.402061e-03 -6.978840e-01 -6.657233e-02 -6.033920e-01 -1.467567e-01
## vard2ltm2.l6 vard2ltp.l6 vard2ltm2.l7 vard2ltp.l7 vard2ltm2.l8
## -5.911775e-01 1.071395e-01 -4.820850e-01 -5.209120e-01 -4.042083e-01
## vard2ltp.l8 vard2ltm2.l9 vard2ltp.l9 vard2ltm2.l10 vard2ltp.l10
## 5.843583e-02 -2.957712e-01 -2.264201e-01 -2.607288e-01 -3.519280e-01
## vard2ltm2.l11 vard2ltp.l11 const
## -1.952368e-01 -4.569036e-02 -1.772883e-05
##
##
## Estimated coefficients for equation vard2ltp:
## =============================================
## Call:
## vard2ltp = vard2ltm2.l1 + vard2ltp.l1 + vard2ltm2.l2 + vard2ltp.l2 + vard2ltm2.l3 + vard2ltp.l3 + vard2ltm2.l4 + vard2ltp.l4 + vard2ltm2.l5 + vard2ltp.l5 + vard2ltm2.l6 + vard2ltp.l6 + vard2ltm2.l7 + vard2ltp.l7 + vard2ltm2.l8 + vard2ltp.l8 + vard2ltm2.l9 + vard2ltp.l9 + vard2ltm2.l10 + vard2ltp.l10 + vard2ltm2.l11 + vard2ltp.l11 + const
##
## vard2ltm2.l1 vard2ltp.l1 vard2ltm2.l2 vard2ltp.l2 vard2ltm2.l3
## -0.0153916910 -0.5768876559 0.0225320104 -0.6496239677 0.0258940415
## vard2ltp.l3 vard2ltm2.l4 vard2ltp.l4 vard2ltm2.l5 vard2ltp.l5
## -0.6720339066 0.0795080689 -0.6540235497 0.0019055836 -0.5936082236
## vard2ltm2.l6 vard2ltp.l6 vard2ltm2.l7 vard2ltp.l7 vard2ltm2.l8
## 0.0257630905 -0.7731697569 -0.0057925819 -0.6635451262 -0.0051972985
## vard2ltp.l8 vard2ltm2.l9 vard2ltp.l9 vard2ltm2.l10 vard2ltp.l10
## -0.6685684171 0.0220922428 -0.5278806069 0.0046915004 -0.4810434376
## vard2ltm2.l11 vard2ltp.l11 const
## 0.0081195814 -0.4276815925 -0.0001442569
summary(var1)
##
## VAR Estimation Results:
## =========================
## Endogenous variables: vard2ltm2, vard2ltp
## Deterministic variables: const
## Sample size: 163
## Log Likelihood: 1316.416
## Roots of the characteristic polynomial:
## 0.9851 0.9851 0.9604 0.9604 0.9425 0.9425 0.9343 0.9343 0.906 0.906 0.8852 0.8852 0.8749 0.8749 0.8717 0.8717 0.8679 0.8553 0.8553 0.8127 0.8127 0.7702
## Call:
## VAR(y = ejvar, p = 11)
##
##
## Estimation results for equation vard2ltm2:
## ==========================================
## vard2ltm2 = vard2ltm2.l1 + vard2ltp.l1 + vard2ltm2.l2 + vard2ltp.l2 + vard2ltm2.l3 + vard2ltp.l3 + vard2ltm2.l4 + vard2ltp.l4 + vard2ltm2.l5 + vard2ltp.l5 + vard2ltm2.l6 + vard2ltp.l6 + vard2ltm2.l7 + vard2ltp.l7 + vard2ltm2.l8 + vard2ltp.l8 + vard2ltm2.l9 + vard2ltp.l9 + vard2ltm2.l10 + vard2ltp.l10 + vard2ltm2.l11 + vard2ltp.l11 + const
##
## Estimate Std. Error t value Pr(>|t|)
## vard2ltm2.l1 -7.630e-01 8.274e-02 -9.221 4.04e-16 ***
## vard2ltp.l1 -1.714e-01 2.356e-01 -0.728 0.468104
## vard2ltm2.l2 -8.434e-01 1.012e-01 -8.333 6.58e-14 ***
## vard2ltp.l2 1.110e-01 2.530e-01 0.438 0.661704
## vard2ltm2.l3 -6.063e-01 1.216e-01 -4.988 1.78e-06 ***
## vard2ltp.l3 -6.402e-03 2.703e-01 -0.024 0.981138
## vard2ltm2.l4 -6.979e-01 1.257e-01 -5.550 1.38e-07 ***
## vard2ltp.l4 -6.657e-02 2.754e-01 -0.242 0.809320
## vard2ltm2.l5 -6.034e-01 1.338e-01 -4.509 1.37e-05 ***
## vard2ltp.l5 -1.468e-01 2.772e-01 -0.529 0.597328
## vard2ltm2.l6 -5.912e-01 1.314e-01 -4.498 1.43e-05 ***
## vard2ltp.l6 1.071e-01 2.444e-01 0.438 0.661785
## vard2ltm2.l7 -4.821e-01 1.316e-01 -3.664 0.000351 ***
## vard2ltp.l7 -5.209e-01 2.800e-01 -1.860 0.064914 .
## vard2ltm2.l8 -4.042e-01 1.261e-01 -3.206 0.001667 **
## vard2ltp.l8 5.844e-02 2.781e-01 0.210 0.833898
## vard2ltm2.l9 -2.958e-01 1.205e-01 -2.455 0.015307 *
## vard2ltp.l9 -2.264e-01 2.731e-01 -0.829 0.408476
## vard2ltm2.l10 -2.607e-01 1.010e-01 -2.580 0.010896 *
## vard2ltp.l10 -3.519e-01 2.542e-01 -1.385 0.168380
## vard2ltm2.l11 -1.952e-01 8.057e-02 -2.423 0.016665 *
## vard2ltp.l11 -4.569e-02 2.370e-01 -0.193 0.847435
## const -1.773e-05 6.388e-04 -0.028 0.977897
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.008133 on 140 degrees of freedom
## Multiple R-Squared: 0.5428, Adjusted R-squared: 0.4709
## F-statistic: 7.555 on 22 and 140 DF, p-value: 6.685e-15
##
##
## Estimation results for equation vard2ltp:
## =========================================
## vard2ltp = vard2ltm2.l1 + vard2ltp.l1 + vard2ltm2.l2 + vard2ltp.l2 + vard2ltm2.l3 + vard2ltp.l3 + vard2ltm2.l4 + vard2ltp.l4 + vard2ltm2.l5 + vard2ltp.l5 + vard2ltm2.l6 + vard2ltp.l6 + vard2ltm2.l7 + vard2ltp.l7 + vard2ltm2.l8 + vard2ltp.l8 + vard2ltm2.l9 + vard2ltp.l9 + vard2ltm2.l10 + vard2ltp.l10 + vard2ltm2.l11 + vard2ltp.l11 + const
##
## Estimate Std. Error t value Pr(>|t|)
## vard2ltm2.l1 -0.0153917 0.0265236 -0.580 0.5626
## vard2ltp.l1 -0.5768877 0.0755409 -7.637 3.16e-12 ***
## vard2ltm2.l2 0.0225320 0.0324482 0.694 0.4886
## vard2ltp.l2 -0.6496240 0.0811166 -8.009 4.05e-13 ***
## vard2ltm2.l3 0.0258940 0.0389673 0.665 0.5075
## vard2ltp.l3 -0.6720339 0.0866516 -7.756 1.65e-12 ***
## vard2ltm2.l4 0.0795081 0.0403071 1.973 0.0505 .
## vard2ltp.l4 -0.6540235 0.0882744 -7.409 1.09e-11 ***
## vard2ltm2.l5 0.0019056 0.0429004 0.044 0.9646
## vard2ltp.l5 -0.5936082 0.0888574 -6.680 5.19e-10 ***
## vard2ltm2.l6 0.0257631 0.0421322 0.611 0.5419
## vard2ltp.l6 -0.7731698 0.0783469 -9.869 < 2e-16 ***
## vard2ltm2.l7 -0.0057926 0.0421757 -0.137 0.8910
## vard2ltp.l7 -0.6635451 0.0897558 -7.393 1.19e-11 ***
## vard2ltm2.l8 -0.0051973 0.0404152 -0.129 0.8979
## vard2ltp.l8 -0.6685684 0.0891632 -7.498 6.74e-12 ***
## vard2ltm2.l9 0.0220922 0.0386188 0.572 0.5682
## vard2ltp.l9 -0.5278806 0.0875485 -6.030 1.39e-08 ***
## vard2ltm2.l10 0.0046915 0.0323905 0.145 0.8850
## vard2ltp.l10 -0.4810434 0.0814811 -5.904 2.56e-08 ***
## vard2ltm2.l11 0.0081196 0.0258292 0.314 0.7537
## vard2ltp.l11 -0.4276816 0.0759902 -5.628 9.59e-08 ***
## const -0.0001443 0.0002048 -0.704 0.4823
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.002607 on 140 degrees of freedom
## Multiple R-Squared: 0.5602, Adjusted R-squared: 0.4911
## F-statistic: 8.107 on 22 and 140 DF, p-value: 5.963e-16
##
##
##
## Covariance matrix of residuals:
## vard2ltm2 vard2ltp
## vard2ltm2 6.615e-05 7.967e-07
## vard2ltp 7.967e-07 6.798e-06
##
## Correlation matrix of residuals:
## vard2ltm2 vard2ltp
## vard2ltm2 1.00000 0.03757
## vard2ltp 0.03757 1.00000
predict(var1)
## $vard2ltm2
## fcst lower upper CI
## [1,] 0.0026504351 -0.01329049 0.01859136 0.01594093
## [2,] -0.0012903644 -0.02138019 0.01879946 0.02008982
## [3,] 0.0004468823 -0.02012240 0.02101617 0.02056929
## [4,] 0.0002362415 -0.02065101 0.02112349 0.02088725
## [5,] -0.0021789296 -0.02329058 0.01893272 0.02111165
## [6,] 0.0014087991 -0.01970894 0.02252654 0.02111774
## [7,] -0.0015125259 -0.02270137 0.01967632 0.02118885
## [8,] -0.0007353639 -0.02217193 0.02070120 0.02143656
## [9,] -0.0001379709 -0.02184007 0.02156413 0.02170210
## [10,] -0.0007812784 -0.02249881 0.02093625 0.02171753
##
## $vard2ltp
## fcst lower upper CI
## [1,] -0.0005427679 -0.005652973 0.004567437 0.005110205
## [2,] 0.0024101137 -0.003499161 0.008319388 0.005909275
## [3,] 0.0021511447 -0.004004144 0.008306434 0.006155289
## [4,] -0.0020013764 -0.008190028 0.004187275 0.006188651
## [5,] 0.0002112159 -0.006001921 0.006424353 0.006213137
## [6,] -0.0036325779 -0.010031449 0.002766293 0.006398871
## [7,] -0.0005470646 -0.007009053 0.005914924 0.006461988
## [8,] -0.0019499228 -0.008423373 0.004523528 0.006473451
## [9,] -0.0012872773 -0.007770857 0.005196302 0.006483579
## [10,] 0.0026061353 -0.003968118 0.009180389 0.006574254
layout(1:2)
plot(var1)
