I'm having a problem with the definition of order of AR, MA and ARMA time series forecasting processes. Imagine we have a time series with data from January to December, and we're in July, trying to predict August. When we say AR(2), are we using lags relating to July and June, or can those two months be any month between January and June?

I tried checking multiple sources but they define order as different things.

CodePudding user response：

The order indicates how many of the previous data points are to be used for forecasting. You use an AR(2) model and want to predict August. That means, the last two data points available and known to you are July und June. If you then want to predict September, your model will use the data from August and July and so on.

You can select the data points with the order. If you simply give a number, all previous data points in that range will be used, e.g. an order of two results in the last 2 lags or an order of 5 results in the last 5 lags. You can also specify the lags in []. An order of [1,3,5] means that your model uses the last, third-last and fifth-last lags, in your case that would be July, May and March, leaving out the second- and fourth-last lag. That would then be an AR([1,3,5]) model.