Time series with SARIMA, how to understand the right seasonality parameter

Question

I'm on my way learning the Time series forecast, but have some doubts.

• As for the ARIMA model, parameters like the p, q can be inferred from the ACF and PACF plotting.
• As for d, this work in combination with the degree of differencing. And, unless I misunderstand, can be left to 0 if the dataserie is already differenced before (e.g. data.diff())

More or less, with the approach above, I am getting decent outputs, but still not very close.

The best I was able to get using the SARIMA model, but I couldn't really find any decent explanation on how to seek for the parameters.

So the logic I used (whether correct or wrong, please tell me) is to use the p parameter as usual, but move the q to Q. Then, there is the s parameter, which more or less I pick in relation of the data. With daily data, I normally look at the peaks and then use a multiple of 7 according to the best performance.

But what for the weekly aggregated data? I had an instance of a dataset where the resulting RSME was getting better only with parameter like p=46 that doesn't sound normal.

Can you please feed me in with some explanation or guide(s) I can use to fill the gaps?

Below there are the initial ACF and PACF plots, for which a p=46 and q=8 demonstrate better prediction than a p=1 and q=8.

Thanks

Answer 1

The simplest way of detecting seasonality is to look for repeated patterns in the ACF/ PACF function, in combination with domain knowledge. For example, a time-series with hourly resolution and daily seasonality (i.e. 24 hours) will show spikes (with exponential decay) at lags 24, 48, 72, etc. I think the correct way to model this is first to model the seasonal component, then examine ACF/ PACF for remaining autocorrelations.

Forecasting: Principles and Practices is a great introductory textbook, accompanied by the forecast package in R. This includes the auto.arima() function, which will automatically find a good (S)ARIMA model to fit your data based on some in-sample criterion such as Akaike's Information Criterion.