Laboratorio 8 SARIMA
Eymi
26 de agosto de 2025
7.1 Ejemplo
d1s=AirPassengers
plot(d1s)
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(forecast)
adf.test(d1s)## Warning in adf.test(d1s): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: d1s
## Dickey-Fuller = -7.3186, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationaryEl comportamiento de los datos es de forma multiplicativa, por loo tanto procedemos a realizar la transformacion de los mismos
d1sl=log(d1s)
plot(d1sl)
adf.test(d1sl)## Warning in adf.test(d1sl): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: d1sl
## Dickey-Fuller = -6.4215, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationaryla serie en logaritmos es estacionario, por que el p valor es menor que alfa
modelo SARIMA
mod=auto.arima(d1sl,trace = T)##
## ARIMA(2,1,2)(1,1,1)[12] : Inf
## ARIMA(0,1,0)(0,1,0)[12] : -434.799
## ARIMA(1,1,0)(1,1,0)[12] : -474.6299
## ARIMA(0,1,1)(0,1,1)[12] : -483.2101
## ARIMA(0,1,1)(0,1,0)[12] : -449.8857
## ARIMA(0,1,1)(1,1,1)[12] : -481.5957
## ARIMA(0,1,1)(0,1,2)[12] : -481.6451
## ARIMA(0,1,1)(1,1,0)[12] : -477.2164
## ARIMA(0,1,1)(1,1,2)[12] : Inf
## ARIMA(0,1,0)(0,1,1)[12] : -467.4644
## ARIMA(1,1,1)(0,1,1)[12] : -481.582
## ARIMA(0,1,2)(0,1,1)[12] : -481.2991
## ARIMA(1,1,0)(0,1,1)[12] : -481.3006
## ARIMA(1,1,2)(0,1,1)[12] : -481.5633
##
## Best model: ARIMA(0,1,1)(0,1,1)[12]mod## Series: d1sl
## ARIMA(0,1,1)(0,1,1)[12]
##
## Coefficients:
## ma1 sma1
## -0.4018 -0.5569
## s.e. 0.0896 0.0731
##
## sigma^2 = 0.001371: log likelihood = 244.7
## AIC=-483.4 AICc=-483.21 BIC=-474.77\((y_t-y_{t-1})-(y_{t-12}-y_{t-13})=-0.40\epsilon_{t-1}-0.5569\epsilon_{t-12}\)
d1slp=predict(mod,3)
d1sp=exp(d1slp$pred)
d1sp## Jan Feb Mar
## 1961 450.4224 425.7172 479.0068ts.plot(d1sp)