My question is about updating the parameters of a regression with ARIMA errors model as new (monthly) data becomes available each month. Similar question were asked here before:
- Updating ARIMA models at frequent intervals
- What do you consider a new model versus an updated model (time series)?
My concern is, when do I know (or how can I test) that my model structure (ARMA terms, exogenous variables) is still suitable? Say in the simplest case my model is y = const + b*x + e, where e ~ ARIMA I estimated in my fitting sample b=-3. A new data point (of the next month) is available and I re-fit the model and obtain b = -3.5 and so on.
When do I know, that something is wrong or how can I continuously (with each update) test my model for consistency?
I know, that the Chow-Test a useful test for model stability. But I always have only one data-point to update.
My idea is:
- Check each month the one-step-ahead forecast with the actual value. If the model gives still reasonable results -> keep it.
- Collect 6 new monthly data points (so half yearly) and check with a Chow-test the model stability between the initial fit-sample and the new sample (6 monthly data points).