#Laboratorio 7 VAR
#Miguel Antonio Garcia
#1310619
library(vars)
## Loading required package: MASS
## Loading required package: strucchange
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
## Loading required package: sandwich
## Loading required package: urca
## Loading required package: lmtest
library(fpp2)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## ── Attaching packages ────────────────────────────────────────────── fpp2 2.5 ──
## ✔ ggplot2 3.4.1 ✔ fma 2.5
## ✔ forecast 8.20 ✔ expsmooth 2.3
##
library(TSA)
## Registered S3 methods overwritten by 'TSA':
## method from
## fitted.Arima forecast
## plot.Arima forecast
##
## Attaching package: 'TSA'
## The following objects are masked from 'package:stats':
##
## acf, arima
## The following object is masked from 'package:utils':
##
## tar
#Cargar datos
series<-uschange
autoplot(uschange[,c(3,5)])
series
## Consumption Income Production Savings Unemployment
## 1970 Q1 0.61598622 0.97226104 -2.45270031 4.81031150 0.9
## 1970 Q2 0.46037569 1.16908472 -0.55152509 7.28799234 0.5
## 1970 Q3 0.87679142 1.55327055 -0.35870786 7.28901306 0.5
## 1970 Q4 -0.27424514 -0.25527238 -2.18545486 0.98522964 0.7
## 1971 Q1 1.89737076 1.98715363 1.90973412 3.65777061 -0.1
## 1971 Q2 0.91199291 1.44733417 0.90153584 6.05134180 -0.1
## 1971 Q3 0.79453885 0.53181193 0.30801942 -0.44583221 0.1
## 1971 Q4 1.64858747 1.16012514 2.29130441 -1.53087186 0.0
## 1972 Q1 1.31372218 0.45701150 4.14957387 -4.35859438 -0.2
## 1972 Q2 1.89147495 1.01662441 1.89062398 -5.05452579 -0.1
## 1972 Q3 1.53071400 1.90410126 1.27335290 5.80995904 -0.2
## 1972 Q4 2.31829471 3.89025866 3.43689207 16.04471706 -0.3
## 1973 Q1 1.81073916 0.70825266 2.79907636 -5.34886849 -0.3
## 1973 Q2 -0.04173996 0.79430954 0.81768862 8.42603436 0.0
## 1973 Q3 0.35423556 0.43381827 0.86899693 2.75879565 -0.1
## 1973 Q4 -0.29163216 1.09380979 1.47296187 11.14642986 0.1
## 1974 Q1 -0.87702794 -1.66168482 -0.88248358 -2.53351449 0.2
## 1974 Q2 0.35113555 -0.93835321 0.07427919 -6.59264464 0.3
## 1974 Q3 0.40959770 0.09448779 -0.41314971 0.51717884 0.5
## 1974 Q4 -1.47580863 -0.12259599 -4.06411893 11.34339540 1.3
## 1975 Q1 0.83225762 -0.16369546 -6.85103912 -5.47619069 1.4
## 1975 Q2 1.65583461 4.53650956 -1.33129558 24.30960536 0.2
## 1975 Q3 1.41942029 -1.46376532 2.42435972 -17.65616104 -0.4
## 1975 Q4 1.05437932 0.76166351 2.16904208 0.64809041 -0.2
## 1976 Q1 1.97998024 1.16825761 3.02720471 -2.95006644 -0.6
## 1976 Q2 0.91391607 0.51729906 1.27881101 -1.47455755 0.0
## 1976 Q3 1.05532326 0.73370026 1.30386487 -0.06754475 0.0
## 1976 Q4 1.29889825 0.59458339 1.77537765 -3.57672239 0.2
## 1977 Q1 1.13637586 -0.03108003 2.05516067 -9.16055658 -0.4
## 1977 Q2 0.54994073 1.23808955 3.05838507 9.09050404 -0.2
## 1977 Q3 0.94985262 1.51880293 1.10308888 7.94495719 -0.4
## 1977 Q4 1.49599724 1.91456240 0.63346850 6.69627648 -0.4
## 1978 Q1 0.57549599 0.70266687 -0.29339056 2.92296383 -0.1
## 1978 Q2 2.11120960 0.98314132 3.94815264 -6.81114259 -0.4
## 1978 Q3 0.41796279 0.71992620 0.87114701 4.79207162 0.1
## 1978 Q4 0.79792710 0.78553605 1.78447991 2.37118400 0.0
## 1979 Q1 0.50584598 1.05755946 0.42594327 7.77418337 -0.2
## 1979 Q2 -0.05775339 -0.86765105 -0.20491944 -5.28634896 -0.1
## 1979 Q3 0.97730010 0.47100340 -0.29723637 -1.84549644 0.2
## 1979 Q4 0.26826982 0.44037974 0.33560928 4.04959810 0.1
## 1980 Q1 -0.15391875 0.33827686 0.41056141 5.86168864 0.3
## 1980 Q2 -2.27411019 -1.46388507 -4.30076832 8.24322919 1.3
## 1980 Q3 1.07188123 1.21301507 -1.64181977 5.70775044 -0.1
## 1980 Q4 1.31644941 1.94243865 3.78045520 9.15098787 -0.3
## 1981 Q1 0.52472770 -0.26813406 0.24627687 -5.68139002 0.2
## 1981 Q2 -0.01728203 -0.02363025 0.30977573 0.88183993 0.1
## 1981 Q3 0.40165150 2.02680183 0.91707444 15.99035721 0.1
## 1981 Q4 -0.75287620 0.19560628 -2.25457797 7.80550650 0.9
## 1982 Q1 0.65938376 0.11969888 -2.07131293 -3.34243955 0.5
## 1982 Q2 0.36854173 0.57548997 -1.24766384 2.19400166 0.6
## 1982 Q3 0.76954464 0.53484410 -1.40050430 0.03499563 0.5
## 1982 Q4 1.80876006 0.44938311 -1.90375664 -9.57651468 0.7
## 1983 Q1 0.96802954 0.85588425 1.14655720 0.34595460 -0.5
## 1983 Q2 1.95946831 0.70632719 2.17942248 -10.17004699 -0.2
## 1983 Q3 1.73949442 1.49810999 3.36771897 0.21217916 -0.9
## 1983 Q4 1.56389332 2.13138911 2.58168445 8.21600068 -0.9
## 1984 Q1 0.84526442 2.02348788 2.89709545 13.86918150 -0.5
## 1984 Q2 1.41504495 1.64921136 1.53821324 4.38900229 -0.6
## 1984 Q3 0.76546608 1.36163845 0.72128740 6.51686089 0.1
## 1984 Q4 1.31380062 0.81927319 0.04115557 -2.87544931 0.0
## 1985 Q1 1.68655320 -0.23895759 0.32353159 -18.71008389 -0.1
## 1985 Q2 0.93436990 1.90677905 0.07020996 11.82871950 0.2
## 1985 Q3 1.90256675 -0.33536283 -0.14046924 -23.57393474 -0.3
## 1985 Q4 0.25656565 1.14181151 0.57978813 11.36628338 -0.1
## 1986 Q1 0.84304279 1.23951110 0.58132135 5.86126836 0.2
## 1986 Q2 1.11177390 1.31938549 -0.57641778 3.27551734 0.0
## 1986 Q3 1.79499406 0.70477150 0.37249329 -10.09044542 -0.2
## 1986 Q4 0.63768446 0.17977925 1.13734778 -4.82920131 -0.4
## 1987 Q1 0.01569397 0.81973366 1.30758228 12.46424452 0.0
## 1987 Q2 1.37731686 -0.97505791 1.75000563 -29.52866718 -0.4
## 1987 Q3 1.15225712 1.80185055 1.84366200 12.32810406 -0.3
## 1987 Q4 0.21016439 1.32743427 2.40645058 16.63076101 -0.2
## 1988 Q1 1.76316026 1.44861875 0.92013121 -0.96896505 0.0
## 1988 Q2 0.73053714 1.02084894 0.87316353 5.67776867 -0.3
## 1988 Q3 0.85083233 0.95820336 0.38103668 3.64649867 0.0
## 1988 Q4 1.13789838 0.96207024 0.70292025 -0.19730358 -0.1
## 1989 Q1 0.46064152 1.22693023 0.43372685 10.01461545 -0.3
## 1989 Q2 0.46937808 -0.29489091 -0.36675732 -8.15576525 0.3
## 1989 Q3 0.98950145 0.67822897 -0.62142121 -2.48622554 0.0
## 1989 Q4 0.43942767 0.80025832 0.42443392 5.44681102 0.1
## 1990 Q1 0.85543417 0.83939484 0.68265169 2.87544931 -0.2
## 1990 Q2 0.31230451 0.59572848 0.77446547 5.10951644 0.0
## 1990 Q3 0.40261313 0.03740765 0.41944800 -3.17767248 0.7
## 1990 Q4 -0.75910716 -0.79479735 -1.57345296 -0.17953326 0.4
## 1991 Q1 -0.34535008 0.21183290 -1.91422028 6.49315257 0.5
## 1991 Q2 0.83564224 0.69043356 0.59131506 -0.30920615 0.1
## 1991 Q3 0.48439843 0.36205181 1.36255645 -0.14086493 0.0
## 1991 Q4 -0.02626579 0.85100324 0.21710308 11.34193010 0.4
## 1992 Q1 1.85996999 2.12421067 -0.13365365 7.23265150 0.1
## 1992 Q2 0.68354371 1.04095059 1.76874773 5.46708666 0.4
## 1992 Q3 1.07661214 0.43562041 0.76167388 -5.93646090 -0.2
## 1992 Q4 1.18372396 0.34210852 1.05024577 -5.88618856 -0.2
## 1993 Q1 0.37817936 0.55877186 0.87901471 2.63464703 -0.4
## 1993 Q2 0.89392729 0.17627103 0.21755108 -6.91664675 0.0
## 1993 Q3 1.09813766 0.05868803 0.40135891 -11.99337844 -0.3
## 1993 Q4 0.88122025 0.65496353 1.49618275 -1.83708870 -0.2
## 1994 Q1 1.14064791 0.69846579 1.22213656 -5.18600629 0.0
## 1994 Q2 0.77176225 1.05367166 1.78250275 5.15609751 -0.4
## 1994 Q3 0.77214364 0.59247377 1.26718100 -2.42215898 -0.2
## 1994 Q4 1.07014805 1.38110661 2.04370404 6.32351898 -0.4
## 1995 Q1 0.26420505 0.94873528 1.02552601 10.11514398 -0.1
## 1995 Q2 0.89311141 0.22780635 0.33785685 -10.60541172 0.2
## 1995 Q3 0.91264702 0.88957006 0.90043887 -0.11570727 0.0
## 1995 Q4 0.70025425 0.57591998 0.87467273 -2.90726686 0.0
## 1996 Q1 0.92360967 0.95255663 0.69285195 2.55933958 -0.1
## 1996 Q2 1.07997887 0.95161791 2.11134752 -0.75802112 -0.2
## 1996 Q3 0.60055799 0.79369738 1.24418680 3.33843952 -0.1
## 1996 Q4 0.78298122 0.52035746 1.35396890 -3.33843952 0.2
## 1997 Q1 1.04949253 0.99858552 1.86714700 0.61269338 -0.2
## 1997 Q2 0.45219855 0.85103564 1.48763922 6.17532322 -0.2
## 1997 Q3 1.69654264 1.18352222 2.28632066 -7.22796452 -0.1
## 1997 Q4 1.18062797 1.42325742 2.48091341 5.43456565 -0.2
## 1998 Q1 1.02693626 2.10753052 1.10343775 19.35335228 0.0
## 1998 Q2 1.75069399 1.38767133 0.65122238 -4.81709478 -0.2
## 1998 Q3 1.30596977 1.01464427 0.72551955 -3.12983982 0.1
## 1998 Q4 1.45888615 0.80893032 1.44421674 -9.14923404 -0.2
## 1999 Q1 0.94821191 0.89173174 1.10341663 1.88735718 -0.2
## 1999 Q2 1.46971415 0.24722185 0.98574261 -23.49652903 0.1
## 1999 Q3 1.12921436 0.66729226 0.90279881 -9.86264835 -0.1
## 1999 Q4 1.45748895 1.46092242 1.75533234 2.35825225 -0.2
## 2000 Q1 1.51106759 1.95061335 0.99682019 12.28684080 0.0
## 2000 Q2 0.95508878 1.03174349 1.23293805 1.28001748 0.0
## 2000 Q3 0.96797647 1.16178668 -0.10225268 2.57390229 -0.1
## 2000 Q4 0.88629738 0.33725343 -0.20388383 -13.16296208 0.0
## 2001 Q1 0.42159086 0.84865826 -1.35143911 13.22491995 0.4
## 2001 Q2 0.25689982 -0.08818148 -1.25954437 -6.89043916 0.2
## 2001 Q3 0.36381084 2.33678920 -1.44101744 41.66826457 0.5
## 2001 Q4 1.51630321 -1.24443353 -1.06013675 -56.75209674 0.7
## 2002 Q1 0.29958257 2.40331419 0.70916406 50.75796205 0.0
## 2002 Q2 0.50899032 0.50559877 1.54280957 0.87861837 0.1
## 2002 Q3 0.69667241 -0.12828194 0.59478143 -14.70397426 -0.1
## 2002 Q4 0.53634306 0.47941927 -0.05776556 1.58733492 0.3
## 2003 Q1 0.43826169 0.27834026 0.53922789 0.49744834 -0.1
## 2003 Q2 1.10719086 1.43729445 -0.69876172 7.00891625 0.4
## 2003 Q3 1.46377882 1.62544947 0.60727351 6.18413150 -0.2
## 2003 Q4 0.77334046 0.40353864 1.00599126 -6.89274778 -0.4
## 2004 Q1 0.96768535 0.72653162 0.65792806 -2.96152040 0.1
## 2004 Q2 0.64760607 0.98056746 0.57461780 8.30885627 -0.2
## 2004 Q3 0.95117167 0.52450113 0.56330030 -8.99318286 -0.2
## 2004 Q4 1.02041702 1.24238706 1.38522763 6.23585017 0.0
## 2005 Q1 0.76172556 -0.96827007 1.39435718 -42.28191228 -0.2
## 2005 Q2 1.08136588 0.78835467 0.50586367 -18.27592893 -0.2
## 2005 Q3 0.77186494 0.51136949 -0.50305848 -7.87665229 0.0
## 2005 Q4 0.37591485 0.82191843 0.93365010 20.37236078 -0.1
## 2006 Q1 1.11522822 2.25904474 0.95057853 37.40653542 -0.2
## 2006 Q2 0.53100554 0.14987813 0.59636010 -12.34810568 -0.1
## 2006 Q3 0.58208747 0.28490722 0.33552773 -10.55276140 -0.1
## 2006 Q4 1.01434389 1.30059162 0.25603401 6.03100080 -0.1
## 2007 Q1 0.52486184 0.65373993 0.91794957 6.60516929 0.0
## 2007 Q2 0.33874119 0.19260870 1.19594247 -7.23648452 0.2
## 2007 Q3 0.44391875 0.26238732 0.22356909 -9.00674555 0.1
## 2007 Q4 0.12505584 0.08392938 0.16424632 2.32887238 0.3
## 2008 Q1 -0.20652548 0.71926565 -0.42872571 29.83728599 0.1
## 2008 Q2 0.16783443 2.08693775 -1.41297022 46.43989041 0.5
## 2008 Q3 -0.72499446 -2.32611860 -3.26349945 -32.53252494 0.5
## 2008 Q4 -1.21068558 0.64019534 -4.35417741 36.31240490 1.2
## 2009 Q1 -0.34354370 -0.18888849 -5.75045075 0.92306020 1.4
## 2009 Q2 -0.45174364 0.70899368 -3.00372447 16.09059408 0.8
## 2009 Q3 0.60491332 -1.10343180 1.39880419 -24.49229966 0.3
## 2009 Q4 -0.01115014 -0.13213193 1.54400617 0.84829220 0.1
## 2010 Q1 0.53481740 0.10094986 1.88006931 -5.54399051 0.0
## 2010 Q2 0.81040406 1.29229259 2.05402479 11.65612884 -0.5
## 2010 Q3 0.64501881 0.49678098 1.42683671 -0.35208609 0.1
## 2010 Q4 1.01833874 0.69495229 0.37927209 -3.27335958 -0.2
## 2011 Q1 0.50041315 1.21571502 0.50174040 14.33860193 -0.3
## 2011 Q2 0.20141978 -0.15658108 0.21878696 -4.07705131 0.1
## 2011 Q3 0.43372599 0.52891255 1.01113866 2.72250400 -0.1
## 2011 Q4 0.33593895 0.06074719 0.85151692 -3.45447712 -0.5
## 2012 Q1 0.60108995 1.62204885 0.88651817 17.62530510 -0.3
## 2012 Q2 0.16942956 0.76689543 0.62923586 8.96949710 0.0
## 2012 Q3 0.26416034 -0.05071452 0.07880166 -3.04922177 -0.4
## 2012 Q4 0.27877186 2.59106697 0.63305509 29.04670355 0.1
## 2013 Q1 0.46861292 -4.26525047 0.67713243 -68.78826698 -0.4
## 2013 Q2 0.20545802 0.58146541 0.30744961 7.81647729 0.0
## 2013 Q3 0.46641787 0.58328912 0.23440888 3.49400682 -0.3
## 2013 Q4 0.83917367 0.21494896 0.79208722 -11.27661450 -0.5
## 2014 Q1 0.47345118 1.10369487 0.54709166 13.52020248 0.0
## 2014 Q2 0.93375698 1.29390492 1.33801074 8.24404770 -0.6
## 2014 Q3 0.91687178 0.99853396 0.62352731 2.46195256 -0.2
## 2014 Q4 1.12533250 1.04641801 0.90355427 -1.51305022 -0.3
## 2015 Q1 0.59624005 0.49040680 -0.46710878 -0.75840017 -0.2
## 2015 Q2 0.70814389 0.95495949 -0.69702162 5.02391773 -0.1
## 2015 Q3 0.66496956 0.80166267 0.38060610 3.18092976 -0.3
## 2015 Q4 0.56167978 0.74006260 -0.84554638 3.48278601 0.0
## 2016 Q1 0.40468216 0.51902540 -0.41793048 2.23653405 0.0
## 2016 Q2 1.04770741 0.72372078 -0.20331883 -2.72150106 -0.1
## 2016 Q3 0.72959779 0.64470081 0.47491844 -0.57285793 0.0
#plot de serie de datos
ts.plot(series[,c(3,5)], xlab="Tiempo",col=c(1,2))
#Búsqueda de parámetros
a <- VARselect(uschange[,c(3,5)], lag.max=15,type="const")
a$selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 10 2 2 10
#Creación de modelo
modelo1<-VAR(uschange[,c(3,5)],p=10,type=c("const"))
modelo_s<-summary(modelo1)
modelo_s
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Production, Unemployment
## Deterministic variables: const
## Sample size: 177
## Log Likelihood: -216.41
## Roots of the characteristic polynomial:
## 0.9173 0.9074 0.9074 0.8857 0.8857 0.884 0.884 0.8821 0.8821 0.8801 0.8801 0.8778 0.8778 0.8752 0.8752 0.8703 0.8527 0.8527 0.3942 0.3942
## Call:
## VAR(y = uschange[, c(3, 5)], p = 10, type = c("const"))
##
##
## Estimation results for equation Production:
## ===========================================
## Production = Production.l1 + Unemployment.l1 + Production.l2 + Unemployment.l2 + Production.l3 + Unemployment.l3 + Production.l4 + Unemployment.l4 + Production.l5 + Unemployment.l5 + Production.l6 + Unemployment.l6 + Production.l7 + Unemployment.l7 + Production.l8 + Unemployment.l8 + Production.l9 + Unemployment.l9 + Production.l10 + Unemployment.l10 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 0.35794 0.11127 3.217 0.00158 **
## Unemployment.l1 -1.78796 0.42396 -4.217 4.18e-05 ***
## Production.l2 -0.14837 0.11280 -1.315 0.19031
## Unemployment.l2 -0.07239 0.44027 -0.164 0.86961
## Production.l3 0.20966 0.11301 1.855 0.06545 .
## Unemployment.l3 0.71328 0.45634 1.563 0.12007
## Production.l4 -0.02368 0.11361 -0.208 0.83518
## Unemployment.l4 0.73752 0.44371 1.662 0.09849 .
## Production.l5 -0.21219 0.11259 -1.885 0.06134 .
## Unemployment.l5 -0.79565 0.44017 -1.808 0.07259 .
## Production.l6 0.01062 0.11229 0.095 0.92476
## Unemployment.l6 -0.56657 0.44444 -1.275 0.20428
## Production.l7 0.07466 0.11196 0.667 0.50588
## Unemployment.l7 0.23374 0.43861 0.533 0.59485
## Production.l8 -0.07852 0.11212 -0.700 0.48475
## Unemployment.l8 1.06355 0.44536 2.388 0.01813 *
## Production.l9 0.18001 0.10620 1.695 0.09206 .
## Unemployment.l9 0.14326 0.42647 0.336 0.73739
## Production.l10 0.13273 0.09750 1.361 0.17535
## Unemployment.l10 0.49355 0.43307 1.140 0.25617
## const 0.21854 0.14348 1.523 0.12974
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 1.111 on 156 degrees of freedom
## Multiple R-Squared: 0.5251, Adjusted R-squared: 0.4643
## F-statistic: 8.626 on 20 and 156 DF, p-value: < 2.2e-16
##
##
## Estimation results for equation Unemployment:
## =============================================
## Unemployment = Production.l1 + Unemployment.l1 + Production.l2 + Unemployment.l2 + Production.l3 + Unemployment.l3 + Production.l4 + Unemployment.l4 + Production.l5 + Unemployment.l5 + Production.l6 + Unemployment.l6 + Production.l7 + Unemployment.l7 + Production.l8 + Unemployment.l8 + Production.l9 + Unemployment.l9 + Production.l10 + Unemployment.l10 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 -0.032185 0.029119 -1.105 0.27073
## Unemployment.l1 0.404708 0.110951 3.648 0.00036 ***
## Production.l2 0.073043 0.029519 2.474 0.01442 *
## Unemployment.l2 0.363820 0.115219 3.158 0.00191 **
## Production.l3 -0.056316 0.029574 -1.904 0.05872 .
## Unemployment.l3 -0.034202 0.119425 -0.286 0.77496
## Production.l4 0.009665 0.029732 0.325 0.74557
## Unemployment.l4 -0.264818 0.116118 -2.281 0.02393 *
## Production.l5 0.054719 0.029466 1.857 0.06519 .
## Unemployment.l5 0.157407 0.115192 1.366 0.17375
## Production.l6 0.011586 0.029386 0.394 0.69392
## Unemployment.l6 0.219150 0.116310 1.884 0.06140 .
## Production.l7 0.020425 0.029301 0.697 0.48680
## Unemployment.l7 0.192913 0.114786 1.681 0.09483 .
## Production.l8 0.024902 0.029342 0.849 0.39736
## Unemployment.l8 -0.244813 0.116551 -2.100 0.03729 *
## Production.l9 -0.090744 0.027792 -3.265 0.00135 **
## Unemployment.l9 -0.181545 0.111606 -1.627 0.10583
## Production.l10 0.026884 0.025515 1.054 0.29367
## Unemployment.l10 -0.022097 0.113334 -0.195 0.84567
## const -0.021177 0.037548 -0.564 0.57357
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.2907 on 156 degrees of freedom
## Multiple R-Squared: 0.4577, Adjusted R-squared: 0.3882
## F-statistic: 6.583 on 20 and 156 DF, p-value: 9.716e-13
##
##
##
## Covariance matrix of residuals:
## Production Unemployment
## Production 1.2342 -0.23115
## Unemployment -0.2311 0.08453
##
## Correlation matrix of residuals:
## Production Unemployment
## Production 1.0000 -0.7156
## Unemployment -0.7156 1.0000
#si no pasan de 1, el modelo es estacionario
modelo_s$roots
## [1] 0.9173477 0.9074411 0.9074411 0.8857057 0.8857057 0.8839837 0.8839837
## [8] 0.8821400 0.8821400 0.8801347 0.8801347 0.8778165 0.8778165 0.8752188
## [15] 0.8752188 0.8702727 0.8527066 0.8527066 0.3942062 0.3942062
summary(modelo1,equation="Consumption")
## Warning in summary.varest(modelo1, equation = "Consumption"):
## Invalid variable name(s) supplied, using first variable.
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Production, Unemployment
## Deterministic variables: const
## Sample size: 177
## Log Likelihood: -216.41
## Roots of the characteristic polynomial:
## 0.9173 0.9074 0.9074 0.8857 0.8857 0.884 0.884 0.8821 0.8821 0.8801 0.8801 0.8778 0.8778 0.8752 0.8752 0.8703 0.8527 0.8527 0.3942 0.3942
## Call:
## VAR(y = uschange[, c(3, 5)], p = 10, type = c("const"))
##
##
## Estimation results for equation Production:
## ===========================================
## Production = Production.l1 + Unemployment.l1 + Production.l2 + Unemployment.l2 + Production.l3 + Unemployment.l3 + Production.l4 + Unemployment.l4 + Production.l5 + Unemployment.l5 + Production.l6 + Unemployment.l6 + Production.l7 + Unemployment.l7 + Production.l8 + Unemployment.l8 + Production.l9 + Unemployment.l9 + Production.l10 + Unemployment.l10 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 0.35794 0.11127 3.217 0.00158 **
## Unemployment.l1 -1.78796 0.42396 -4.217 4.18e-05 ***
## Production.l2 -0.14837 0.11280 -1.315 0.19031
## Unemployment.l2 -0.07239 0.44027 -0.164 0.86961
## Production.l3 0.20966 0.11301 1.855 0.06545 .
## Unemployment.l3 0.71328 0.45634 1.563 0.12007
## Production.l4 -0.02368 0.11361 -0.208 0.83518
## Unemployment.l4 0.73752 0.44371 1.662 0.09849 .
## Production.l5 -0.21219 0.11259 -1.885 0.06134 .
## Unemployment.l5 -0.79565 0.44017 -1.808 0.07259 .
## Production.l6 0.01062 0.11229 0.095 0.92476
## Unemployment.l6 -0.56657 0.44444 -1.275 0.20428
## Production.l7 0.07466 0.11196 0.667 0.50588
## Unemployment.l7 0.23374 0.43861 0.533 0.59485
## Production.l8 -0.07852 0.11212 -0.700 0.48475
## Unemployment.l8 1.06355 0.44536 2.388 0.01813 *
## Production.l9 0.18001 0.10620 1.695 0.09206 .
## Unemployment.l9 0.14326 0.42647 0.336 0.73739
## Production.l10 0.13273 0.09750 1.361 0.17535
## Unemployment.l10 0.49355 0.43307 1.140 0.25617
## const 0.21854 0.14348 1.523 0.12974
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 1.111 on 156 degrees of freedom
## Multiple R-Squared: 0.5251, Adjusted R-squared: 0.4643
## F-statistic: 8.626 on 20 and 156 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## Production Unemployment
## Production 1.2342 -0.23115
## Unemployment -0.2311 0.08453
##
## Correlation matrix of residuals:
## Production Unemployment
## Production 1.0000 -0.7156
## Unemployment -0.7156 1.0000
summary(modelo1,equation="Income")
## Warning in summary.varest(modelo1, equation = "Income"):
## Invalid variable name(s) supplied, using first variable.
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Production, Unemployment
## Deterministic variables: const
## Sample size: 177
## Log Likelihood: -216.41
## Roots of the characteristic polynomial:
## 0.9173 0.9074 0.9074 0.8857 0.8857 0.884 0.884 0.8821 0.8821 0.8801 0.8801 0.8778 0.8778 0.8752 0.8752 0.8703 0.8527 0.8527 0.3942 0.3942
## Call:
## VAR(y = uschange[, c(3, 5)], p = 10, type = c("const"))
##
##
## Estimation results for equation Production:
## ===========================================
## Production = Production.l1 + Unemployment.l1 + Production.l2 + Unemployment.l2 + Production.l3 + Unemployment.l3 + Production.l4 + Unemployment.l4 + Production.l5 + Unemployment.l5 + Production.l6 + Unemployment.l6 + Production.l7 + Unemployment.l7 + Production.l8 + Unemployment.l8 + Production.l9 + Unemployment.l9 + Production.l10 + Unemployment.l10 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 0.35794 0.11127 3.217 0.00158 **
## Unemployment.l1 -1.78796 0.42396 -4.217 4.18e-05 ***
## Production.l2 -0.14837 0.11280 -1.315 0.19031
## Unemployment.l2 -0.07239 0.44027 -0.164 0.86961
## Production.l3 0.20966 0.11301 1.855 0.06545 .
## Unemployment.l3 0.71328 0.45634 1.563 0.12007
## Production.l4 -0.02368 0.11361 -0.208 0.83518
## Unemployment.l4 0.73752 0.44371 1.662 0.09849 .
## Production.l5 -0.21219 0.11259 -1.885 0.06134 .
## Unemployment.l5 -0.79565 0.44017 -1.808 0.07259 .
## Production.l6 0.01062 0.11229 0.095 0.92476
## Unemployment.l6 -0.56657 0.44444 -1.275 0.20428
## Production.l7 0.07466 0.11196 0.667 0.50588
## Unemployment.l7 0.23374 0.43861 0.533 0.59485
## Production.l8 -0.07852 0.11212 -0.700 0.48475
## Unemployment.l8 1.06355 0.44536 2.388 0.01813 *
## Production.l9 0.18001 0.10620 1.695 0.09206 .
## Unemployment.l9 0.14326 0.42647 0.336 0.73739
## Production.l10 0.13273 0.09750 1.361 0.17535
## Unemployment.l10 0.49355 0.43307 1.140 0.25617
## const 0.21854 0.14348 1.523 0.12974
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 1.111 on 156 degrees of freedom
## Multiple R-Squared: 0.5251, Adjusted R-squared: 0.4643
## F-statistic: 8.626 on 20 and 156 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## Production Unemployment
## Production 1.2342 -0.23115
## Unemployment -0.2311 0.08453
##
## Correlation matrix of residuals:
## Production Unemployment
## Production 1.0000 -0.7156
## Unemployment -0.7156 1.0000
#Validación del modelo
#>PortManteu Test > 0.05 Autocorrelación
serial.test(modelo1, lags.pt=10, type="PT.asymptotic")
##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 7.9607, df = 0, p-value < 2.2e-16
#RaÃz unitaria < 1
roots(modelo1)
## [1] 0.9173477 0.9074411 0.9074411 0.8857057 0.8857057 0.8839837 0.8839837
## [8] 0.8821400 0.8821400 0.8801347 0.8801347 0.8778165 0.8778165 0.8752188
## [15] 0.8752188 0.8702727 0.8527066 0.8527066 0.3942062 0.3942062
#normalidad Jarque Bera < 0.05
normality.test(modelo1, multivariate.only=FALSE)
## $Production
##
## JB-Test (univariate)
##
## data: Residual of Production equation
## Chi-squared = 23.285, df = 2, p-value = 8.783e-06
##
##
## $Unemployment
##
## JB-Test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 20.166, df = 2, p-value = 4.178e-05
##
##
## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 27.34, df = 4, p-value = 1.697e-05
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 6.1498, df = 2, p-value = 0.0462
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 21.19, df = 2, p-value = 2.504e-05
#heteroscedasticity >0.05 NO HAY
arch<-arch.test(modelo1, lags.multi = 12, multivariate.only = FALSE)
arch
## $Production
##
## ARCH test (univariate)
##
## data: Residual of Production equation
## Chi-squared = 48.387, df = 16, p-value = 4.129e-05
##
##
## $Unemployment
##
## ARCH test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 17.175, df = 16, p-value = 0.3744
##
##
##
## ARCH (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 120.62, df = 108, p-value = 0.1915
#Structural breaks
stab<-stability(modelo1, type = "OLS-CUSUM")
par(mar=c(1,1,1,1))
plot(stab)
#BoxCox.ar(abs(uschange[,2]))
#Causalidad de granger
#granger < 0.05 para que exista causalidad
GrangerIncome <-causality(modelo1, cause = 'Production')
GrangerIncome
## $Granger
##
## Granger causality H0: Production do not Granger-cause Unemployment
##
## data: VAR object modelo1
## F-Test = 2.346, df1 = 10, df2 = 312, p-value = 0.0111
##
##
## $Instant
##
## H0: No instantaneous causality between: Production and Unemployment
##
## data: VAR object modelo1
## Chi-squared = 59.945, df = 1, p-value = 9.77e-15
GrangerConsumptions <-causality(modelo1, cause = 'Unemployment')
GrangerConsumptions
## $Granger
##
## Granger causality H0: Unemployment do not Granger-cause Production
##
## data: VAR object modelo1
## F-Test = 3.0085, df1 = 10, df2 = 312, p-value = 0.001207
##
##
## $Instant
##
## H0: No instantaneous causality between: Unemployment and Production
##
## data: VAR object modelo1
## Chi-squared = 59.945, df = 1, p-value = 9.77e-15
#Respuesta de impulso
#Como se comporta una variable si la otra variable recibe un "shock"
IncomeIRF <- irf(modelo1, impulse = "Unemployment", response="Production", n.ahead = 20, boot = T )
plot(IncomeIRF, ylab = "Production", main = "Shock desde Consumptions")
ConsumptionIRF <- irf(modelo1, impulse = "Production", response="Unemployment", n.ahead = 20, boot = T )
plot(ConsumptionIRF, ylab = "Employment", main = "Shock desde Income")
#Descomposición de la varianza
FEVD1 <- fevd(modelo1, n.ahead = 10)
plot(FEVD1)
#prediccion
fore<-predict(modelo1, n.ahead = 10, ci=0.95)
fanchart(fore)
autoplot(forecast(modelo1))
#Formula
modelo1$varresult$Production$coefficients
## Production.l1 Unemployment.l1 Production.l2 Unemployment.l2
## 0.35794466 -1.78795512 -0.14837359 -0.07239060
## Production.l3 Unemployment.l3 Production.l4 Unemployment.l4
## 0.20966005 0.71327696 -0.02367755 0.73751673
## Production.l5 Unemployment.l5 Production.l6 Unemployment.l6
## -0.21219489 -0.79564846 0.01062115 -0.56657405
## Production.l7 Unemployment.l7 Production.l8 Unemployment.l8
## 0.07465883 0.23374471 -0.07852426 1.06354859
## Production.l9 Unemployment.l9 Production.l10 Unemployment.l10
## 0.18001097 0.14325690 0.13272984 0.49355258
## const
## 0.21853835
modelo1$varresult$Unemployment$coefficients
## Production.l1 Unemployment.l1 Production.l2 Unemployment.l2
## -0.032185400 0.404708014 0.073042623 0.363819674
## Production.l3 Unemployment.l3 Production.l4 Unemployment.l4
## -0.056316091 -0.034202127 0.009665045 -0.264817743
## Production.l5 Unemployment.l5 Production.l6 Unemployment.l6
## 0.054718872 0.157407334 0.011585955 0.219149685
## Production.l7 Unemployment.l7 Production.l8 Unemployment.l8
## 0.020424724 0.192913120 0.024902498 -0.244812966
## Production.l9 Unemployment.l9 Production.l10 Unemployment.l10
## -0.090743629 -0.181545014 0.026883602 -0.022097372
## const
## -0.021176611
autoplot(forecast(modelo1))