Periodogram model selection with multiple candidate periods

[Marius G]

Hi Chris,

first, thanks for developing an maintaining this amazing package! I have a question regarding model comparison for periodicity in movement data. Specifically, I would like to compare two periodogram models that were fit with differing harmonic structures, e.g. one including 24 h + 12 h harmonics and another including 24 h + 8 h harmonics.

A naïve approach would be to fit a combined model including all three harmonics (24 h, 12 h, 8 h), but this becomes increasingly challenging and potentially overfits the data when exploring multiple candidate periods. I am therefore wondering whether there is a principled way to compare these models beyond visual assessment.

Would you recommend any alternative approaches? For example, comparing predictive performance (e.g., MSPE or similar) or using another information-theoretic or likelihood-based metric?

Best,

Marius

[Christen Fleming]

Hi Marius,

I would recommend comparing the MSPE for different trend models (and the same auto-covariance model). Likelihood-based metrics are too aggressive in supporting trend terms that over-fit to the data.

Best,

Chris