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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

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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.

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  • $\begingroup$ yes, it is! I am now writing a paper, and I considered many cases, including the one you mentioned as a special case. But since I am not very knowledgable in the time series modeling field, I hope to see if anyone has done this. I google a lot and cannot find anything. $\endgroup$ – ArtificiallyIntelligence Sep 25 '18 at 21:06
  • $\begingroup$ After half a year... Here is the arXiv! arxiv.org/abs/1902.05198 $\endgroup$ – ArtificiallyIntelligence Feb 19 at 20:12

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