I have monthly climate data for 90 years.
I assembled the best model I could (added sensible parameters to minimize AIC), and then tried various ARMA correlation structures (using
gls in lmne package in R) to reduce significant small (<30) lags. I then selected the ARMA model with the lowest AIC as my best model.
However, based on the ACF and PACF plots, there are still significant larger-interval lags (>30).
My questions are:
How should I react to that? Do I consider them to be important or spurious?
- I initially assumed that if lag 60 (associated with 5 year) was significant, then this would indicate that there is a 5 year trend in my data. However, I thought I'd heard before that ACF/PACF is not a good way to approach long-term lags.
What do I do with this? How would I go about reducing the larger lags?
For example, is there a specific ARMA p/q combo that 'best' reduces larger lags? Or should I try adding sin/cos variables in my model? Or some other approach?
Again, if the ACF/PACF are not good for IDing large lags, how would I determine the 'real' long-term cyclic patterns to actually account for?