# Should I choose an ARIMA model (2,1,1) with a higher AIC value or an ARIMA model (6,1,8) with a lower AIC value?

I am trying to fit an ARIMA model to time series data. When I fit the model using auto.arima function in R, ARIMA(2,1,1) model is selected with AIC=6618.16. However, when I played around with the model, I found that ARIMA(6,1,8) gives an AIC=6528.37. Which one should I choose? Here are the ACF and PACF plots after one regular differentiation.

Besides, a portmanteau test (Ljung-Box test) gives the following results for checking the residuals whether are white noise or not. A portmanteau test returns a large p-value, also suggesting that the residuals are white noise (Forecasting: Principles and Practice by Rob J Hyndman and George Athanasopoulos).

Ljung-Box test

data:  Residuals from ARIMA(6,1,8)
Q* = 6.2381, df = 3, p-value = 0.1006

Model df: 14.   Total lags used: 17

Ljung-Box test

data:  Residuals from ARIMA(2,1,1)
Q* = 20.261, df = 7, p-value = 0.005033

Model df: 3.   Total lags used: 10


• Thanks for the recommendation. auto.arima chose ARIMA(9,1,1) which has a lower AIC than ARIMA(2,1,1). However, the cross-validation error of ARIMA(2,1,1) was lower than that of ARIMA(9,1,1). Nevertheless, when I checked the residuals by using the Ljung-Box test (using checkresiduals(ARIMA.model) function in R), I realized that the residuals of ARIMA(9,1,1) are white noise, but not ARIMA(2,1,1). This raises another question in my mind. Feb 14 at 18:33