Assessing seasonality. When to use seasonal ARIMA instead of non-seasonal ARIMA?

Question

I need to test the effect of some predictors over the oil price. I'm fitting ARIMA models to my data.

Could you help me determine whether using a seasonal or a non-seasonal ARIMA model? Is oil price known to be seasonal?

Generally speaking, if I'm not sure about seasonality in my data, what is the best way to test it? Is there a specific test I can use? Or do I just put a variable that indicates the month in a regression model and see whether it is significant predictor?

I found some answers here: What method can be used to detect seasonality in data? But still I'm wondering if there's a specific statistical test I can use.

Answer 1

A decent methodology is that employed by the automated (S)ARIMA model selector function auto.arima in "forecast" package in R. It is described in a paper by Hyndman & Khandakar "Automatic time series for forecasting: the forecast package for R" (2008). The method has been employed widely and seems to be quite popular. Its performance has been evaluated on a large set of time series and has been good, as documented in Rob J. Hyndman's blog post "R vs Autobox vs ForecastPro vs …" (see Table 1 and Table 2).

So how does it work? There are two aspects to seasonality in SARIMA modelling: seasonal differencing and seasonal AR and MA patterns. First, auto.arima uses OCSB (or optionally Canova-Hansen) test to determine whether there is a need for seasonal differencing. Second, auto.arima determines the "optimal" lag orders of SAR and SMA by doing a local search of models with different lag orders and selecting the one that minimizes the AICc (or optionally AIC or BIC).

Answer 2

I know seasonal ARIMA model that involves seasonal difference, seasonal AR and MA terms can handle data with seasonality. If your mission is to compare forecasting performance of several models, using X-13 to de-seasonise series might be a good idea.