I computed an algorithm to find out the best ARMA (p,q) model via minimisation of the AIC. It turned out ARMA(5,5) is the best one with AIC=-2693.12.
However, the inverse roots of the AR and MA characteristic polynomial are the following:
Many of them looks very close to the unitary circle. That makes me feel like I'm in presence of a near non-stationarity & invertibility series (isn't it?). However ACF and PACF show the model as great for capturing autocorrelation in the residuals.
If I use
auto.arima() in $R$ to find the best p,q instead, it turns out the best model is a simple AR(1). The AIC worst off to -2687.08.
By looking on internet I figured out that
auto.arima() looks yes at AIC (if you specify so) but also at "numerical stability" in returning the "optimal" orders p,q.
What fools me is:
- What does it mean? What are the implication for a statistical analysis?
- Which order should I use? Should I trade some AIC "points" in exchange of much numerical stability proposed by
- Would the previous answer change in case the scope of my ARMA model is forecasting or testing?
dput() of my dataset for replicability.