# Is there any theory on the order of Autoregression model for periodic time series? [closed]

Say M periodic signals, then one can safely say using AR-M model can achieve the perfect prediction. But how about further, in a more general sense, is there any publications on this?

## Update:

Here is my arXiv paper on this problem https://arxiv.org/abs/1902.05198

If you have a perfectly predictable signal periodic in frequency $$f$$, the pattern repeats every cycle, or $$1/f$$ time units.
You need a single lag to predict it, the series lagged by $$1/f$$ time units. So AR-$$1/f$$ model will achieve perfect prediction, where the only lag included is the one mentioned.