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I have a number of time series which are derived of same underlying data. However, the data in each comes from a different source, so they may be slightly lagged or differently enriched but essentially representing the same underlying data.

Is it possible to find out if there is one of these series that is odd and severely delayed or out of line?

As an example, imagine you subscribing to market data for the same stock from 5 different providers and trying to find out which is running slow in a dynamic way. However, stock prices are very deterministic so that makes the problem slightly simplified. In my case I am working on data that doesn't have a single source to check.

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Cross-correlation analysis can be conducted to determine the presence of leading or lagged variables. See for example the discussion in this post and the example in this other post. A more detailed description of the overall idea can be found here. Some technical details for the implementation of this approach in the R software are discussed in this post.

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You might want to look at How to statistically compare two time series? as it treats the question of discriminating between time series. Essentially a common model is used to estimate parameters both globally AND individually. The error sums of squares are then compared to determine if a significan reduction is obtained by individual estimation as compared to global estimation. Upon concluding that there are benefits from individual estimation one needs to identify which ones are different from the "others" . This is akin to finding which means are different from other means.

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  • $\begingroup$ hmm i have considered granger earlier but i was thinking since i have multiple such series.. i might as well do a z-score on first 3 moments to find the odd one out.. does that sound like it will pick up the odd one? $\endgroup$
    – ramneek handa
    Commented Sep 16, 2013 at 15:27
  • $\begingroup$ I don't see how this proposed solution would work. Exactly what estimate(s) in your model would change if you were to apply it to a series whose times were additively shifted, and how would you use those estimates to determine whether the times were shifted forwards or backwards? For simplicity, let's suppose that neither series exhibits any "pulses," "level shifts," or secular trends. $\endgroup$
    – whuber ♦
    Commented Sep 16, 2013 at 15:32
  • $\begingroup$ @whuber I don't understand your comment and/or the question. Perhaps we should chat offline on this. $\endgroup$
    – IrishStat
    Commented Oct 15, 2013 at 16:25

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