library(vars)
## Warning: package 'vars' was built under R version 4.1.3
## Loading required package: MASS
## Warning: package 'MASS' was built under R version 4.1.3
## 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
## Warning: package 'lmtest' was built under R version 4.1.3
library(forecast)
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(seasonal)
library(tseries)
## Warning: package 'tseries' was built under R version 4.1.3
library(fpp2)
## -- Attaching packages ---------------------------------------------- fpp2 2.4 --
## v ggplot2 3.3.5 v expsmooth 2.3
## v fma 2.4
##
data(h02)
h02
## Jan Feb Mar Apr May Jun Jul
## 1991 0.4297950
## 1992 0.6601190 0.3362200 0.3513480 0.3798080 0.3618010 0.4105340 0.4833887
## 1993 0.7515028 0.3875543 0.4272832 0.4138902 0.4288588 0.4701264 0.5092097
## 1994 0.8193253 0.4376698 0.5061213 0.4704912 0.5106963 0.5405138 0.5581189
## 1995 0.8031126 0.4752582 0.5525723 0.5271078 0.5612498 0.5889776 0.6231336
## 1996 0.9372759 0.5287616 0.5593399 0.5778717 0.6149274 0.5941888 0.7077584
## 1997 0.8468335 0.4638225 0.4852732 0.5280586 0.5623365 0.5885704 0.6694804
## 1998 0.8005444 0.4905572 0.5244080 0.5366495 0.5520905 0.6033656 0.6812454
## 1999 0.8930815 0.5126960 0.6529959 0.5739764 0.6392384 0.7038719 0.7706482
## 2000 0.9696557 0.5732915 0.6185068 0.6189957 0.6652092 0.7265201 0.8558649
## 2001 1.0438053 0.5106472 0.6725690 0.6484701 0.7041147 0.6994307 0.8519259
## 2002 1.1458676 0.5755844 0.6411646 0.6798621 0.7679384 0.7520959 0.9180636
## 2003 1.0781449 0.5782962 0.6433333 0.6633674 0.7505160 0.8007456 0.9163610
## 2004 1.1301252 0.6679887 0.7490143 0.7399860 0.7951286 0.8568028 1.0015932
## 2005 1.1706900 0.5976390 0.6525900 0.6705050 0.6952480 0.8422630 0.8743360
## 2006 1.2306910 0.5871350 0.7069590 0.6396410 0.8074050 0.7979700 0.8843120
## 2007 1.2233190 0.5977530 0.7043980 0.5617600 0.7452580 0.8379340 0.9541440
## 2008 1.2199410 0.7618220 0.6494350 0.8278870 0.8162550 0.7621370
## Aug Sep Oct Nov Dec
## 1991 0.4009060 0.4321590 0.4925430 0.5023690 0.6026520
## 1992 0.4754634 0.5347610 0.5686061 0.5952233 0.7712578
## 1993 0.5584430 0.6015141 0.6329471 0.6996054 0.9630805
## 1994 0.6728521 0.6858974 0.6896920 0.7413036 0.8133076
## 1995 0.7408372 0.7253718 0.8158030 0.8140095 0.9266531
## 1996 0.7195020 0.7443237 0.8048551 0.7885423 0.9710894
## 1997 0.6779937 0.7629955 0.7997237 0.7705219 0.9943893
## 1998 0.6780753 0.7948926 0.7846239 0.8130087 0.9777323
## 1999 0.8461859 0.8927289 0.8978999 0.9472807 1.0507073
## 2000 0.8659843 0.8252488 0.9554210 0.9385960 1.0130244
## 2001 0.9077052 0.8674445 1.0242928 1.1095902 1.0123132
## 2002 0.9243675 1.0131977 1.0269761 1.0067960 1.1027757
## 2003 0.9168868 1.0846589 1.1506482 1.0508382 1.2232345
## 2004 0.9948643 1.1344320 1.1810110 1.2160370 1.2572380
## 2005 1.0064970 1.0947360 1.0270430 1.1492320 1.1607120
## 2006 1.0496480 0.9957090 1.1682530 1.1080380 1.1200530
## 2007 1.0782195 1.1109816 1.1099791 1.1635343 1.1765890
## 2008
data("h02")
plot(h02)
autoplot(h02) + ylab("Retail index") + xlab("Year")
plot(decompose(h02))
adf.test(h02)
## Warning in adf.test(h02): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: h02
## Dickey-Fuller = -9.5147, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary
# Si el p-value es menor a 0.05, es estacionaria.
h02%>% diff(lag=12) %>% ggtsdisplay()
modelo1 = arima(h02, order=c(5,1,3), seasonal = c(1,1,1))
modelo1$aic
## [1] -560.0981
modelo1
##
## Call:
## arima(x = h02, order = c(5, 1, 3), seasonal = c(1, 1, 1))
##
## Coefficients:
## ar1 ar2 ar3 ar4 ar5 ma1 ma2 ma3 sar1
## -0.2137 -0.1500 0.4109 0.0943 0.1305 -0.635 0.2504 -0.5247 0.1322
## s.e. 0.5254 0.3723 0.1993 0.2230 0.2222 0.533 0.6179 0.3663 0.1292
## sma1
## -0.6455
## s.e. 0.0983
##
## sigma^2 estimated as 0.002685: log likelihood = 291.05, aic = -560.1
h02 %>%
arima(order=c(5,1,3), seasonal=c(1,1,1)) %>%
residuals() %>% ggtsdisplay()
checkresiduals(modelo1)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(5,1,3)(1,1,1)[12]
## Q* = 28.135, df = 14, p-value = 0.01365
##
## Model df: 10. Total lags used: 24
autoplot(forecast(modelo1, h=36))
forecast(modelo1, h=36)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jul 2008 1.0250499 0.9586497 1.0914501 0.9234996 1.1266002
## Aug 2008 1.0222376 0.9550811 1.0893941 0.9195306 1.1249446
## Sep 2008 1.0971237 1.0240698 1.1701776 0.9853973 1.2088500
## Oct 2008 1.1755844 1.0981577 1.2530110 1.0571705 1.2939982
## Nov 2008 1.1429267 1.0652178 1.2206357 1.0240811 1.2617723
## Dec 2008 1.2019186 1.1211046 1.2827326 1.0783242 1.3255130
## Jan 2009 1.2480676 1.1659002 1.3302349 1.1224034 1.3737317
## Feb 2009 0.7031284 0.6205317 0.7857251 0.5768076 0.8294492
## Mar 2009 0.7136212 0.6296585 0.7975840 0.5852113 0.8420312
## Apr 2009 0.7669704 0.6823418 0.8515991 0.6375421 0.8963988
## May 2009 0.8186169 0.7334846 0.9037493 0.6884183 0.9488156
## Jun 2009 0.8319892 0.7460988 0.9178795 0.7006312 0.9633471
## Jul 2009 1.0094074 0.9140650 1.1047498 0.8635938 1.1552210
## Aug 2009 1.0600729 0.9637034 1.1564424 0.9126884 1.2074573
## Sep 2009 1.1197445 1.0205193 1.2189697 0.9679926 1.2714964
## Oct 2009 1.1793310 1.0778906 1.2807715 1.0241912 1.3344708
## Nov 2009 1.1749833 1.0728289 1.2771378 1.0187516 1.3312151
## Dec 2009 1.2203714 1.1163446 1.3243983 1.0612761 1.3794667
## Jan 2010 1.2602733 1.1550730 1.3654736 1.0993834 1.4211632
## Feb 2010 0.7190557 0.6130936 0.8250179 0.5570007 0.8811108
## Mar 2010 0.7353631 0.6282216 0.8425047 0.5715043 0.8992220
## Apr 2010 0.7727313 0.6647392 0.8807234 0.6075716 0.9378909
## May 2010 0.8372405 0.7284762 0.9460047 0.6708998 1.0035811
## Jun 2010 0.8547744 0.7451237 0.9644251 0.6870782 1.0224707
## Jul 2010 1.0224617 0.9055516 1.1393718 0.8436632 1.2012602
## Aug 2010 1.0811144 0.9629732 1.1992556 0.9004331 1.2617958
## Sep 2010 1.1368846 1.0161169 1.2576523 0.9521863 1.3215829
## Oct 2010 1.1950256 1.0720432 1.3180079 1.0069403 1.3831109
## Nov 2010 1.1943838 1.0704432 1.3183244 1.0048330 1.3839346
## Dec 2010 1.2373387 1.1114797 1.3631978 1.0448539 1.4298236
## Jan 2011 1.2769287 1.1496999 1.4041574 1.0823491 1.4715082
## Feb 2011 0.7360260 0.6077960 0.8642560 0.5399151 0.9321368
## Mar 2011 0.7529353 0.6233429 0.8825277 0.5547408 0.9511298
## Apr 2011 0.7883998 0.6577238 0.9190757 0.5885482 0.9882514
## May 2011 0.8544824 0.7227988 0.9861659 0.6530897 1.0558750
## Jun 2011 0.8725441 0.7397522 1.0053359 0.6694565 1.0756316