I am seeking to characterize time-series data (specifically parameters derived from sensor data) for 18 patients collected over 20 days using autocorrelation (see plot below of autocorrelation functions for 18 patients for a given sensor parameter).

I want to see if I can use the autocorrelation function values at different lag values (days in this case) to distinguish between time-series.

Autocorrelation function of time-series

Is correlating the autocorrelation value at a given lag with another parameter (e.g. patient age or patient outcome measure) a statistically valid approach?

Can autocorrelation be used to infer the statistical relationship between day-to-day measurements of the sensor data?


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    $\begingroup$ What do you mean by "valid"? What do you mean by "the relationship"? It all depends on the details of your problem and the assumptions you're willing to make. $\endgroup$ – A. Donda Nov 29 '13 at 18:19
  • $\begingroup$ If I understand you correctly, you want to estimate a sequence of autocorrelation coefficients $\{\alpha_k^i\}_{k=1}^{20}$ for each patient $i \in \{1,\ldots,18\},$ and then relate these coefficients to other features of patient $i$. Per se, this seems viable. However I don't think that estimating the $\alpha_k^i$'s ``freely'' from a sample of just 20 data points per patient is a promising way to go (the estimates will be highly unstable). Instead you might want to impose some more structure on the problem (either over time - e.g. impose an AR(1) for each patient - or across patients). $\endgroup$ – Fabian Nov 29 '13 at 22:33
  • $\begingroup$ @Fabian, thanks for your comment. Your summery is correct. I am actually calculating the ACF from 60 data points but I am only examining 20 as that is the range of interest. $\endgroup$ – BGreene Nov 29 '13 at 23:49
  • $\begingroup$ @A.Donda, by valid I mean statistically valid. Relationship in the sense of correlation, as detailed above. $\endgroup$ – BGreene Nov 29 '13 at 23:51
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    $\begingroup$ @BGreene, 60 sounds a lot better than 20 for estimating the autocorrelations. However, for your next step (regressing the ac coefs on patient features), your sample size would be only 18...and estimating these regressions separately for each autocorrelation lag seems quite inefficient (not exploiting the full dynamics of the data). I think that a full model (which specifies what is going on both over time and across patients) would be more elegant here. Maybe some kind of (dynamic) panel data model could be useful. $\endgroup$ – Fabian Nov 30 '13 at 23:31