I have $500$ time-series that represent different occurences of the same class of events. As such they have similar properties but not the same length (lengths vary from 30 to 150). I suspect the general structure of the time-series of being a $AR(2)$ model.

From what I know, the packages in R and Python can compute the auto-regression coefficients only if being fed a single time-serious.

What I tried to do is computing the coefficients for each time-series and then taking the weighted average of those coefficients (weighted by each time-series length) but I'm not really convinced by this method.

Does anyone have any ideas about a proper and clean way to find auto-regression coefficients for mutiple time-series with different lengths?

Any help would be much appreciated. Thank you very much.

  • $\begingroup$ You write of a suspicion of "the general structure" of the series. Even if they are all AR(2), do you have grounds to suspect they all have the same autoregressive parameters? Do they all have the same innovation variance? Are they dependent in any way? $\endgroup$ – S. Kolassa - Reinstate Monica Jul 10 at 13:03
  • $\begingroup$ There is no dependence. I don't have grounds to suppose that the parameters are the same or that the innovation variance is the same besides my knowledge of the origin of the data and that it should be consistent. And anyway, I can't make such a hypothesis and compute the parameters regardless? $\endgroup$ – jamesCA Jul 10 at 13:11
  • $\begingroup$ If you can't suppose that the series share the same AR parameters, then why do you want to take an average? If you don't know anything about your series and how they hang together, there does not seem to be anything you can learn from series A to apply to series B. $\endgroup$ – S. Kolassa - Reinstate Monica Jul 10 at 13:13
  • $\begingroup$ If I knew that the parameters are close (and supposed to be equal), then taking the average wouldn't have been such a bad idea? $\endgroup$ – jamesCA Jul 10 at 13:22
  • $\begingroup$ If you believe they are equal, then taking averages is an excellent idea. (Weighting may or may not help. If at all, the weights should probably rather reflect the standard errors of the parameter estimates, which includes both the series length and the variance of the innovations.) If you just assume they are close together, then perhaps some sort of Bayesian approach may help. $\endgroup$ – S. Kolassa - Reinstate Monica Jul 10 at 13:32

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