Laboratorio 7 - Kenet Gálvez_1111919
Kenet Gálvez
2023-03-15
Se cargan las bases de datos ‘uschange’ de donde se evaluarán el modelos VAR para caracterizar las interacciones simultaneas entre el grupo de las variables.
Datos del modelo.
series<-uschange
autoplot(uschange)
autoplot(uschange[, c(2,5)])
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 0.0Gráfica de las variables seleccionadas:
ts.plot(series[, c(2,5)], ylab ="Valores", xlab="Tiempo", main="Comportamiento de las variables",col=c(1,2))
Selección de parámetros:
a <- VARselect(uschange[, c(2,5)], lag.max=15,type="const")
a$selection## AIC(n) HQ(n) SC(n) FPE(n)
## 8 1 1 8Creación de modelo:
modelo1<-VAR(uschange[, c(2,5)],p=5,type=c("const"))
modelo_s<-summary(modelo1)Evaluando estacionalidad:
modelo_s$roots## [1] 0.7775660 0.7775660 0.7660914 0.7660914 0.7488061 0.7488061 0.6720236
## [8] 0.6720236 0.6364359 0.5646411Dado que los valores obtenidos no son mayores a 1, se afirma que el modelo tiene estacionariedad.
Datos del modelo por cada variable:
summary(modelo1,equation="Income")##
## VAR Estimation Results:
## =========================
## Endogenous variables: Income, Unemployment
## Deterministic variables: const
## Sample size: 182
## Log Likelihood: -262.292
## Roots of the characteristic polynomial:
## 0.7776 0.7776 0.7661 0.7661 0.7488 0.7488 0.672 0.672 0.6364 0.5646
## Call:
## VAR(y = uschange[, c(2, 5)], p = 5, type = c("const"))
##
##
## Estimation results for equation Income:
## =======================================
## Income = Income.l1 + Unemployment.l1 + Income.l2 + Unemployment.l2 + Income.l3 + Unemployment.l3 + Income.l4 + Unemployment.l4 + Income.l5 + Unemployment.l5 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Income.l1 -0.13069 0.07628 -1.713 0.08848 .
## Unemployment.l1 -0.47812 0.22736 -2.103 0.03693 *
## Income.l2 0.08289 0.07790 1.064 0.28883
## Unemployment.l2 0.39251 0.23868 1.644 0.10191
## Income.l3 0.03524 0.07602 0.464 0.64351
## Unemployment.l3 -0.65814 0.24414 -2.696 0.00773 **
## Income.l4 -0.09359 0.07556 -1.239 0.21717
## Unemployment.l4 -0.14117 0.24531 -0.575 0.56571
## Income.l5 -0.12761 0.07471 -1.708 0.08944 .
## Unemployment.l5 0.39764 0.22214 1.790 0.07522 .
## const 0.87038 0.14889 5.846 2.49e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.8936 on 171 degrees of freedom
## Multiple R-Squared: 0.1347, Adjusted R-squared: 0.08413
## F-statistic: 2.663 on 10 and 171 DF, p-value: 0.004781
##
##
##
## Covariance matrix of residuals:
## Income Unemployment
## Income 0.7985 -0.05280
## Unemployment -0.0528 0.09033
##
## Correlation matrix of residuals:
## Income Unemployment
## Income 1.0000 -0.1966
## Unemployment -0.1966 1.0000summary(modelo1,equation="Unemployment")##
## VAR Estimation Results:
## =========================
## Endogenous variables: Income, Unemployment
## Deterministic variables: const
## Sample size: 182
## Log Likelihood: -262.292
## Roots of the characteristic polynomial:
## 0.7776 0.7776 0.7661 0.7661 0.7488 0.7488 0.672 0.672 0.6364 0.5646
## Call:
## VAR(y = uschange[, c(2, 5)], p = 5, type = c("const"))
##
##
## Estimation results for equation Unemployment:
## =============================================
## Unemployment = Income.l1 + Unemployment.l1 + Income.l2 + Unemployment.l2 + Income.l3 + Unemployment.l3 + Income.l4 + Unemployment.l4 + Income.l5 + Unemployment.l5 + const
##
## Estimate Std. Error t value Pr(>|t|)
## Income.l1 -0.050174 0.025657 -1.956 0.05215 .
## Unemployment.l1 0.436087 0.076472 5.703 5.08e-08 ***
## Income.l2 -0.004766 0.026202 -0.182 0.85589
## Unemployment.l2 0.156143 0.080280 1.945 0.05342 .
## Income.l3 -0.023081 0.025569 -0.903 0.36796
## Unemployment.l3 0.067925 0.082118 0.827 0.40930
## Income.l4 -0.012685 0.025414 -0.499 0.61833
## Unemployment.l4 -0.183030 0.082510 -2.218 0.02785 *
## Income.l5 0.068785 0.025128 2.737 0.00685 **
## Unemployment.l5 0.038701 0.074718 0.518 0.60516
## const 0.012796 0.050080 0.256 0.79863
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
##
## Residual standard error: 0.3006 on 171 degrees of freedom
## Multiple R-Squared: 0.3665, Adjusted R-squared: 0.3295
## F-statistic: 9.893 on 10 and 171 DF, p-value: 5.479e-13
##
##
##
## Covariance matrix of residuals:
## Income Unemployment
## Income 0.7985 -0.05280
## Unemployment -0.0528 0.09033
##
## Correlation matrix of residuals:
## Income Unemployment
## Income 1.0000 -0.1966
## Unemployment -0.1966 1.0000Validación del modelo:
Valuando autocorrelación - PortManteu Test:
serial.test(modelo1, lags.pt=11, type="PT.asymptotic")##
## Portmanteau Test (asymptotic)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 35.653, df = 24, p-value = 0.05929A través de la prueba se obtuvo un p-value de 0.05929, que es mayor a 0.05, con lo que se determina que sí existe autocorrelación.
Valuando normalidad - Jarque vera:
normality.test(modelo1, multivariate.only=FALSE)## $Income
##
## JB-Test (univariate)
##
## data: Residual of Income equation
## Chi-squared = 195.51, df = 2, p-value < 2.2e-16
##
##
## $Unemployment
##
## JB-Test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 33.197, df = 2, p-value = 6.184e-08
##
##
## $JB
##
## JB-Test (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 216.79, df = 4, p-value < 2.2e-16
##
##
## $Skewness
##
## Skewness only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 7.8916, df = 2, p-value = 0.01934
##
##
## $Kurtosis
##
## Kurtosis only (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 208.9, df = 2, p-value < 2.2e-16A través de la prueba se obtuvo un p-value de 2.2e-16, que es menor a 0.05, con lo que se determina que sí existe normalidad en el comportamiento de los residuos del modelo.
Valuando heteroscedasticidad - prueva ARCH:
arch<-arch.test(modelo1, lags.multi = 12, multivariate.only = FALSE)
arch## $Income
##
## ARCH test (univariate)
##
## data: Residual of Income equation
## Chi-squared = 11.621, df = 16, p-value = 0.7697
##
##
## $Unemployment
##
## ARCH test (univariate)
##
## data: Residual of Unemployment equation
## Chi-squared = 21.391, df = 16, p-value = 0.164
##
##
##
## ARCH (multivariate)
##
## data: Residuals of VAR object modelo1
## Chi-squared = 121.69, df = 108, p-value = 0.1737A través de la prueba se obtuvo un p-value de 0.1737, que es mayor a 0.05, con lo que se determina que no existe heteroscedasticidad en el comportamiento del modelo, por lo que la varianza de los residuos del modelo sí son constantes.
Valuando choques estructurales:
stab<-stability(modelo1, type = "OLS-CUSUM")
par(mar=c(1,1,1,1))
plot(stab)
Gráfica de OLSCUSUM
plot(stab)
Dentro de la gráfica se muestra que los valores no superan los límites de tolerancia, de esta manera se determina que hay estabilidad en el modelo.
Valuando causalidad - Granger:
Income
GrangerIncome <-causality(modelo1, cause = 'Income')
GrangerIncome## $Granger
##
## Granger causality H0: Income do not Granger-cause Unemployment
##
## data: VAR object modelo1
## F-Test = 2.8057, df1 = 5, df2 = 342, p-value = 0.01687
##
##
## $Instant
##
## H0: No instantaneous causality between: Income and Unemployment
##
## data: VAR object modelo1
## Chi-squared = 6.7734, df = 1, p-value = 0.009253El resultado muestra que el p-value es 0.01687, que es menor a 0.05. Esto determina que hay causalidad de la variable ‘income’ a la variable ‘unemployment’.
Unemployment
GrangerUnemployment <-causality(modelo1, cause = 'Unemployment')
GrangerUnemployment## $Granger
##
## Granger causality H0: Unemployment do not Granger-cause Income
##
## data: VAR object modelo1
## F-Test = 3.7264, df1 = 5, df2 = 342, p-value = 0.002681
##
##
## $Instant
##
## H0: No instantaneous causality between: Unemployment and Income
##
## data: VAR object modelo1
## Chi-squared = 6.7734, df = 1, p-value = 0.009253El resultado muestra que el p-value es 0.002681, que es menor a 0.05. Esto determina que hay causalidad de la variable ‘unemployment’ a la variable ‘income’.
Comportmiento de las variables al recibir un ‘shock’:
Shock entre las variable
Al recibir un shock en los valores, la intención es imponer comportamientos atípicos y demostrar que en el largo plazo las variables vuelven a entrelazarse, como se muestra en las siguientes gráficas, donde se demuestra que sí son compatibles.
Income
IncomeIRF <- irf(modelo1, impulse = "Unemployment", response="Income", n.ahead = 20, boot = T )
plot(IncomeIRF, ylab = "Income", main = "Shock desde Unemployment")
Unemployment
UnemploymentIRF <- irf(modelo1, impulse = "Income", response="Unemployment", n.ahead = 20, boot = T )
plot(UnemploymentIRF, ylab = "Unemployment", main = "Shock desde Income")
Descomposición de la varianza:
FEVD1 <- fevd(modelo1, n.ahead = 10)
plot(FEVD1)
Al observar la gráfica anterior la variable ‘Unemployment’ explica en un porcentaje muy bajo a la variable ‘income’. Por otra parte, se obtiene el mismo resultado desde la variable ‘income’ respecto de la la variable ‘Unemployment’. Esto indica que para el pronóstico de las variables se recomienda evaluarlas en distintos modelos, cada una por separado.
Predicción:
fore<-predict(modelo1, n.ahead = 10, ci=0.95)
fanchart(fore)
Gráfica de la predicción
autoplot(forecast(modelo1))
Fórmula:
modelo1$varresult$Income$coefficients## Income.l1 Unemployment.l1 Income.l2 Unemployment.l2 Income.l3
## -0.13068647 -0.47812026 0.08288524 0.39250556 0.03524393
## Unemployment.l3 Income.l4 Unemployment.l4 Income.l5 Unemployment.l5
## -0.65813631 -0.09359142 -0.14117449 -0.12760511 0.39764021
## const
## 0.87038486modelo1$varresult$Consumption$coefficients## NULLautoplot(forecast(modelo1))