1. Utilizando los datos uschange de la librería fpp2, utilice las columnas Savings, Unemployment y Production. Utilizando los modelos VAR genere una predicción de los siguientes 2 años.
library(vars)
## Warning: package 'vars' was built under R version 4.1.3
## 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(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.6 v dplyr 1.0.7
## v tidyr 1.2.0 v stringr 1.4.0
## v readr 2.1.2 v forcats 0.5.1
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x stringr::boundary() masks strucchange::boundary()
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()
## x dplyr::select() masks MASS::select()
library(ggfortify)
library(forecast)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## Registered S3 methods overwritten by 'forecast':
## method from
## autoplot.Arima ggfortify
## autoplot.acf ggfortify
## autoplot.ar ggfortify
## autoplot.bats ggfortify
## autoplot.decomposed.ts ggfortify
## autoplot.ets ggfortify
## autoplot.forecast ggfortify
## autoplot.stl ggfortify
## autoplot.ts ggfortify
## fitted.ar ggfortify
## fortify.ts ggfortify
## residuals.ar ggfortify
library(seasonal)
##
## Attaching package: 'seasonal'
## The following object is masked from 'package:tibble':
##
## view
library(tseries)
library(fpp2)
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v fma 2.4 v expsmooth 2.3
##
# Cargar datos
series<-uschange
?uschange
## starting httpd help server ...
## done
uschange
## 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
autoplot(uschange[,3:5])
# Plot de serie de datos
ts.plot(uschange[,c(3,4,5)], xlab="Tiempo",col=c(3,4,5))
# Busqueda de parametros
selection <-VARselect(uschange[,c(3,4,5)], lag.max=15,type="const")
selection$selection
## AIC(n) HQ(n) SC(n) FPE(n)
## 2 2 1 2
# Creacion del modelo
modelo1<-VAR(uschange[,c(3,4,5)],p=2,type=c("const"))
modelo1
##
## VAR Estimation Results:
## =======================
##
## Estimated coefficients for equation Production:
## ===============================================
## Call:
## Production = Production.l1 + Savings.l1 + Unemployment.l1 + Production.l2 + Savings.l2 + Unemployment.l2 + const
##
## Production.l1 Savings.l1 Unemployment.l1 Production.l2 Savings.l2
## 0.443231138 -0.009833695 -1.253057668 -0.057492433 -0.010006992
## Unemployment.l2 const
## 0.530690891 0.350422160
##
##
## Estimated coefficients for equation Savings:
## ============================================
## Call:
## Savings = Production.l1 + Savings.l1 + Unemployment.l1 + Production.l2 + Savings.l2 + Unemployment.l2 + const
##
## Production.l1 Savings.l1 Unemployment.l1 Production.l2 Savings.l2
## -2.05568244 -0.29606465 -6.81463534 1.78019819 -0.02382193
## Unemployment.l2 const
## 7.99531280 1.67866777
##
##
## Estimated coefficients for equation Unemployment:
## =================================================
## Call:
## Unemployment = Production.l1 + Savings.l1 + Unemployment.l1 + Production.l2 + Savings.l2 + Unemployment.l2 + const
##
## Production.l1 Savings.l1 Unemployment.l1 Production.l2 Savings.l2
## -0.036884554 0.002444545 0.337627743 0.025596317 0.001637642
## Unemployment.l2 const
## 0.197630824 -0.001302766
summary(modelo1,equation="Savings")
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Production, Savings, Unemployment
## Deterministic variables: const
## Sample size: 185
## Log Likelihood: -1000.283
## Roots of the characteristic polynomial:
## 0.6559 0.4112 0.399 0.399 0.3189 0.3189
## Call:
## VAR(y = uschange[, c(3, 4, 5)], p = 2, type = c("const"))
##
##
## Estimation results for equation Savings:
## ========================================
## Savings = Production.l1 + Savings.l1 + Unemployment.l1 + Production.l2 + Savings.l2 + Unemployment.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 -2.05568 1.08290 -1.898 0.059272 .
## Savings.l1 -0.29606 0.07501 -3.947 0.000114 ***
## Unemployment.l1 -6.81464 4.25954 -1.600 0.111405
## Production.l2 1.78020 1.05732 1.684 0.093996 .
## Savings.l2 -0.02382 0.07441 -0.320 0.749235
## Unemployment.l2 7.99531 4.35419 1.836 0.067991 .
## const 1.67867 1.19945 1.400 0.163393
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 13.01 on 178 degrees of freedom
## Multiple R-Squared: 0.1321, Adjusted R-squared: 0.1028
## F-statistic: 4.515 on 6 and 178 DF, p-value: 0.0002765
##
##
##
## Covariance matrix of residuals:
## Production Savings Unemployment
## Production 1.441 -1.5606 -0.26799
## Savings -1.561 169.1681 0.55216
## Unemployment -0.268 0.5522 0.09667
##
## Correlation matrix of residuals:
## Production Savings Unemployment
## Production 1.00000 -0.09996 -0.7181
## Savings -0.09996 1.00000 0.1365
## Unemployment -0.71807 0.13654 1.0000
summary(modelo1,equation="Unemployment")
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Production, Savings, Unemployment
## Deterministic variables: const
## Sample size: 185
## Log Likelihood: -1000.283
## Roots of the characteristic polynomial:
## 0.6559 0.4112 0.399 0.399 0.3189 0.3189
## Call:
## VAR(y = uschange[, c(3, 4, 5)], p = 2, type = c("const"))
##
##
## Estimation results for equation Unemployment:
## =============================================
## Unemployment = Production.l1 + Savings.l1 + Unemployment.l1 + Production.l2 + Savings.l2 + Unemployment.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 -0.036885 0.025887 -1.425 0.15595
## Savings.l1 0.002445 0.001793 1.363 0.17453
## Unemployment.l1 0.337628 0.101825 3.316 0.00111 **
## Production.l2 0.025596 0.025275 1.013 0.31258
## Savings.l2 0.001638 0.001779 0.921 0.35848
## Unemployment.l2 0.197631 0.104087 1.899 0.05922 .
## const -0.001303 0.028673 -0.045 0.96381
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.3109 on 178 degrees of freedom
## Multiple R-Squared: 0.3155, Adjusted R-squared: 0.2925
## F-statistic: 13.68 on 6 and 178 DF, p-value: 9.504e-13
##
##
##
## Covariance matrix of residuals:
## Production Savings Unemployment
## Production 1.441 -1.5606 -0.26799
## Savings -1.561 169.1681 0.55216
## Unemployment -0.268 0.5522 0.09667
##
## Correlation matrix of residuals:
## Production Savings Unemployment
## Production 1.00000 -0.09996 -0.7181
## Savings -0.09996 1.00000 0.1365
## Unemployment -0.71807 0.13654 1.0000
summary(modelo1,equation="Production")
##
## VAR Estimation Results:
## =========================
## Endogenous variables: Production, Savings, Unemployment
## Deterministic variables: const
## Sample size: 185
## Log Likelihood: -1000.283
## Roots of the characteristic polynomial:
## 0.6559 0.4112 0.399 0.399 0.3189 0.3189
## Call:
## VAR(y = uschange[, c(3, 4, 5)], p = 2, type = c("const"))
##
##
## Estimation results for equation Production:
## ===========================================
## Production = Production.l1 + Savings.l1 + Unemployment.l1 + Production.l2 + Savings.l2 + Unemployment.l2 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Production.l1 0.443231 0.099938 4.435 1.61e-05 ***
## Savings.l1 -0.009834 0.006923 -1.420 0.15722
## Unemployment.l1 -1.253058 0.393103 -3.188 0.00169 **
## Production.l2 -0.057492 0.097578 -0.589 0.55648
## Savings.l2 -0.010007 0.006867 -1.457 0.14681
## Unemployment.l2 0.530691 0.401838 1.321 0.18831
## const 0.350422 0.110694 3.166 0.00182 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 1.2 on 178 degrees of freedom
## Multiple R-Squared: 0.409, Adjusted R-squared: 0.389
## F-statistic: 20.53 on 6 and 178 DF, p-value: < 2.2e-16
##
##
##
## Covariance matrix of residuals:
## Production Savings Unemployment
## Production 1.441 -1.5606 -0.26799
## Savings -1.561 169.1681 0.55216
## Unemployment -0.268 0.5522 0.09667
##
## Correlation matrix of residuals:
## Production Savings Unemployment
## Production 1.00000 -0.09996 -0.7181
## Savings -0.09996 1.00000 0.1365
## Unemployment -0.71807 0.13654 1.0000
# Validacion del modelo
# >PortManteu Test > 0.05
serial.test(modelo1, lags.pt=15, type="PT.asymptotic")
##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 138.69, df = 117, p-value = 0.08351
roots(modelo1)
## [1] 0.6558793 0.4112444 0.3989926 0.3989926 0.3189046 0.3189046
normality.test(modelo1, multivariate.only=FALSE)
## $Production
##
## JB-Test (univariate)
##
## data: Residual of Production equation
## Chi-squared = 44.717, df = 2, p-value = 1.949e-10
##
##
## $Savings
##
## JB-Test (univariate)
##
## data: Residual of Savings equation
## Chi-squared = 149.08, df = 2, p-value < 2.2e-16
##
##
## $Unemployment
##
## JB-Test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 33.933, df = 2, p-value = 4.282e-08
##
##
## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 187.43, df = 6, p-value < 2.2e-16
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 3.8415, df = 3, p-value = 0.2791
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 183.59, df = 3, p-value < 2.2e-16
#Prueba grafica
plot(modelo1, names="Savings")
dev.off()
## null device
## 1
par(mar=c(1,1,1,1))
acf(residuals(modelo1)[,1])
pacf(residuals(modelo1)[,1])
#Formula
modelo1$varresult$Savings$coefficients
## Production.l1 Savings.l1 Unemployment.l1 Production.l2 Savings.l2
## -2.05568244 -0.29606465 -6.81463534 1.78019819 -0.02382193
## Unemployment.l2 const
## 7.99531280 1.67866777
modelo1$varresult$Unemployment$coefficients
## Production.l1 Savings.l1 Unemployment.l1 Production.l2 Savings.l2
## -0.036884554 0.002444545 0.337627743 0.025596317 0.001637642
## Unemployment.l2 const
## 0.197630824 -0.001302766
modelo1$varresult$Production$coefficients
## Production.l1 Savings.l1 Unemployment.l1 Production.l2 Savings.l2
## 0.443231138 -0.009833695 -1.253057668 -0.057492433 -0.010006992
## Unemployment.l2 const
## 0.530690891 0.350422160
# Comparacion con otros modelos
modelo2<-VAR(uschange[,1:2],p=2,type=c("const"))
modelo3<-VAR(uschange[,1:2],p=3,type=c("const"))
aic1<-summary(modelo1)$logLik
aic1
## [1] -1000.283
aic2<-summary(modelo2)$logLik
aic2
## [1] -388.9931
aic3<-summary(modelo3)$logLik
aic3
## [1] -380.1549
autoplot(uschange[,c(3,4,5)])