Interpretation of PACF and ACF plots [duplicate]

Question

I am trying to fit an ARMA model to a time series of a power spectral density values that I have calculated.

Here is the plot of the data:

with corresponding autocorrelation and partial autocorrelation plots

I am fairly new to time series analysis but the way I am interpreting it is as follows:

The slowly varying ACF (it hits zero around lag 55) indicates non stationarity initially, but since there are significant spikes in the PACF for the first few lags, this indicates that the PACF may explain the behaviour of the ACF and we in fact need more AR terms. In this case there seem to be significant AR lags in the first 5 and so this would suggest a possible ARMA(5,0) model?

However I have also read that the amount of MA terms you need correspond to the first lag outside of the confidence interval where each following lag decay to 0 - hence might I need an ARMA(5,1) model?

As a third problem to my the data looks like it may be somewhat periodic, if this is the case how do you go about fitting an ARMA model?

Answer 1

Forecasting: Principles and Practice, section 8.5 offers some very rough guidance on using ACF/PACF plots to fit models. In your specific case, it looks like you may have an ARIMA($p$,$d$,$q$) process with both $p\neq 0$ and $q\neq 0$. In this case, the (P)ACF plots are not helpful for selecting model orders.

I suggest that you use a more modern method, by fitting different models and choosing the one that minimizes an information criterion like the AIC.