LAB 5

MODELOS ARIMA

data("h02")
plot(h02)

autoplot(h02) + ylab("Retail index") + xlab("Year")

plot(decompose(h02))

adf.test(h02) # p-value<.05 para que sea estacionaria

## 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

h02 %>% diff(lag=12) %>% ggtsdisplay()

#h02 %>% diff(lag=4) %>% diff() %>% ggtsdisplay()

modelo1 = arima(h02, order=c(6,1,0), seasonal = c(0,1,1))
modelo2 = arima(h02, order=c(7,1,0), seasonal = c(0,1,1))
modelo3 = arima(h02, order=c(8,1,0), seasonal = c(0,1,1))
modelo11 = arima(h02, order=c(9,1,0), seasonal = c(0,1,1))


modelo4 = arima(h02, order=c(0,1,3), seasonal = c(1,1,0))
modelo5 = arima(h02, order=c(0,1,7), seasonal = c(1,1,0))
modelo6 = arima(h02, order=c(0,1,8), seasonal = c(1,1,0))
modelo7 = arima(h02, order=c(0,1,3), seasonal = c(0,1,1))
modelo8 = arima(h02, order=c(3,1,0), seasonal = c(0,1,1))
modelo9 = arima(h02, order=c(4,1,0), seasonal = c(0,1,1))
modelo10 = arima(h02, order=c(5,1,0), seasonal = c(0,1,1))


modelo1$aic

## [1] -560.826

modelo2$aic

## [1] -558.8793

modelo3$aic

## [1] -566.55

modelo4$aic

## [1] -543.0077

modelo5$aic

## [1] -546.7135

modelo6$aic

## [1] -544.7808

modelo7$aic

## [1] -560.1133

modelo8$aic

## [1] -558.806

modelo9$aic

## [1] -560.1863

modelo10$aic

## [1] -560.5159

modelo11$aic

## [1] -564.5826

modelo1

## 
## Call:
## arima(x = h02, order = c(6, 1, 0), seasonal = c(0, 1, 1))
## 
## Coefficients:
##           ar1      ar2      ar3      ar4      ar5      ar6     sma1
##       -0.8366  -0.4064  -0.0864  -0.2659  -0.2071  -0.1163  -0.5614
## s.e.   0.0760   0.1009   0.1027   0.0977   0.0958   0.0762   0.0686
## 
## sigma^2 estimated as 0.002775:  log likelihood = 288.41,  aic = -560.83

h02 %>%
  arima(order=c(8,1,0), seasonal=c(0,1,1)) %>%
  residuals() %>% ggtsdisplay()

checkresiduals(modelo3)

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(8,1,0)(0,1,1)[12]
## Q* = 14.541, df = 15, p-value = 0.485
## 
## Model df: 9.   Total lags used: 24

forecast(modelo3, h=36)

##          Point Forecast     Lo 80     Hi 80     Lo 95     Hi 95
## Jul 2008      1.0163371 0.9507271 1.0819471 0.9159953 1.1166790
## Aug 2008      1.0087800 0.9421827 1.0753772 0.9069283 1.1106316
## Sep 2008      1.0933572 1.0205622 1.1661521 0.9820268 1.2046875
## Oct 2008      1.1582676 1.0797191 1.2368161 1.0381380 1.2783971
## Nov 2008      1.1672075 1.0883132 1.2461018 1.0465491 1.2878659
## Dec 2008      1.1922043 1.1096304 1.2747783 1.0659184 1.3184903
## Jan 2009      1.2751472 1.1917785 1.3585159 1.1476458 1.4026486
## Feb 2009      0.7062200 0.6221120 0.7903281 0.5775879 0.8348522
## Mar 2009      0.7071514 0.6219105 0.7923924 0.5767867 0.8375162
## Apr 2009      0.7710448 0.6829203 0.8591693 0.6362700 0.9058197
## May 2009      0.7992269 0.7098370 0.8886169 0.6625168 0.9359371
## Jun 2009      0.8410115 0.7490571 0.9329660 0.7003793 0.9816437
## Jul 2009      1.0028361 0.8995262 1.1061459 0.8448373 1.1608348
## Aug 2009      1.0505036 0.9453379 1.1556693 0.8896665 1.2113407
## Sep 2009      1.1211665 1.0106591 1.2316740 0.9521599 1.2901732
## Oct 2009      1.1736061 1.0596660 1.2875463 0.9993497 1.3478625
## Nov 2009      1.1867274 1.0711234 1.3023315 1.0099263 1.3635286
## Dec 2009      1.2163130 1.0974583 1.3351678 1.0345404 1.3980857
## Jan 2010      1.2763552 1.1555729 1.3971375 1.0916347 1.4610758
## Feb 2010      0.7159096 0.5931948 0.8386245 0.5282335 0.9035858
## Mar 2010      0.7336670 0.6086487 0.8586852 0.5424681 0.9248659
## Apr 2010      0.7729530 0.6450399 0.9008661 0.5773268 0.9685791
## May 2010      0.8249395 0.6949136 0.9549654 0.6260821 1.0237970
## Jun 2010      0.8592767 0.7263165 0.9922368 0.6559317 1.0626216
## Jul 2010      1.0162430 0.8737578 1.1587283 0.7983307 1.2341554
## Aug 2010      1.0739873 0.9287189 1.2192557 0.8518184 1.2961561
## Sep 2010      1.1373671 0.9870908 1.2876433 0.9075394 1.3671947
## Oct 2010      1.1886583 1.0343394 1.3429771 0.9526480 1.4246686
## Nov 2010      1.2037992 1.0470670 1.3605314 0.9640979 1.4435004
## Dec 2010      1.2333617 1.0728955 1.3938278 0.9879499 1.4787734
## Jan 2011      1.2895826 1.1265322 1.4526329 1.0402186 1.5389465
## Feb 2011      0.7347579 0.5691426 0.9003732 0.4814711 0.9880447
## Mar 2011      0.7497139 0.5812660 0.9181618 0.4920950 1.0073328
## Apr 2011      0.7884261 0.6166490 0.9602032 0.5257157 1.0511365
## May 2011      0.8441710 0.6696773 1.0186647 0.5773060 1.1110361
## Jun 2011      0.8749520 0.6971789 1.0527252 0.6030714 1.1468327

autoplot(forecast(modelo3, h=36))

LAB 5

Ostin Molina

27/2/2022

MODELOS ARIMA

Explicación