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Suppose, I have several hundred time series that are originating from one system and probably correlate. Now suppose, one of the signals, lets say signal A, shows strange behavior at several timestamps, behavior that leads to an error thrown (like exceed a certain threshold). My final goal is to predict the occurrence of these errors from the most correlating signals. I can't use all signals for the prediction, because as said, there are several hundred of them and I suspect most won't play a role in the error development in signal A.

I want to find the X signals that correlate the most with these behaviors in signal A. That "error-dependend-correlation" might be totally independent from the correlation of the signals in a non-error scenario. So, I'm not interested in the correlation of the signals under normal conditions, but only in the correlation in an error case. So a correlation should be more important, if it shows up around the timestamp (mostly before, but also shortly after).

Does a normal cross correlation make any sense here? Or are there any other techniques to solve this?

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  • $\begingroup$ I think it does, however, it would not help in prediction. You should correlate the series of interest $y_t$ with lagged series $x_t$ for different $x$s, that would be relevant for prediction. You would only include $t$s that correspond to "errors" in in $y$. $\endgroup$ – Richard Hardy Nov 22 '18 at 13:45
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I think you can determine a dataset whose columns are your time series and add a further column as indicator (NO, YES) of the error/anomaly you want to predict.

You can split such dataset in a training and test dataset as made of subsets of time contiguous values. Then, you can fit your model by taking advantage of partial least square learning algorithm, capable to reveal the most influential x‐variables with respect to the predicted response.

As predictors you may choose any time series value at current time except the one where such errors/anomalies occurs. You may anyway include as predictors lagged values from any of your time series.

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