# ARIMA comparison: Is a low AIC better than a low MASE

I have a dataset for the daily USD/DKK exchange rate for the past 10 years. my training set consists of the first 9 years and my test set consists of the last year. I am trying to choose between the following to two ARIMA models. 1. arima (1,0,1)

   # Arima (1,0,1)
n <- 2332  # length(train_ts)
m <- 259   # AVG numbers of observations a year
y <- ts(rnorm(n) + (1:n)%%100/30, f=m)

fit3 <- auto.arima(y, seasonal=FALSE, xreg=fourier(y, K=4))
fit3
fit4 <- Arima(train_ts, order= c(1,0,1), xreg = fourier(y, K=4))

autoplot(forecast(fit4, h=2*m, xreg=fourier(y, K=4, h=2*m))) + autolayer(test_ts, series= "Test data")


AIC=-8495.16 AICc=-8495.02 BIC=-8426.1 and the MASE for the test set: 0.3655065

1. arima model (2, 1, 3)

arima_fit <- Arima(train_ts, order = c(2, 1, 3), include.constant = FALSE) arima_fit

AIC=-8505.87 AICc=-8505.84 BIC=-8471.35 and the MASE for the test set: 0.63749344

My thought is to go with the first model, becuase the AIC is simulair, but the MASE is much lower, but I dont know if I am wrong.

Can anybody help me decide which model to go with, and tell me if I should only look at AIC and BIC when comparing ARIMA models?

• I don't think the choice between validation metrics is the problem here since both models are clearly very bad. These results are expected since you're choosing low-order nonseasonal models to forecast a seasonal time series. How did you come up with these models and what does auto.arima give you? – Digio Nov 30 '17 at 13:17
• since it is daily data with a long seasonal period, i had to use this the code i got from this article to run the auto.arima (robjhyndman.com/hyndsight/longseasonality). would you suggest to take monthly data instead in order to better account for the seasonality? – Martin Brummerstedt Nov 30 '17 at 15:43
• Yes, I think you should try it on monthly data without the xreg option. – Digio Dec 1 '17 at 13:24
• thanks i tried it with the monthly data and the auto.arima returned an arima (0,1,0) without seasonality. – Martin Brummerstedt Dec 1 '17 at 19:37
• Care to share this data? – Digio Dec 4 '17 at 9:02