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I have two sensors logging data synchronously. The two sensors are similar, so the recorded time series are correlated except for some special conditions.

I recorded data in different input parameter conditions of the system. And I would like to combine the two time series in one. The objective of this combination is to increase the sensitivity to system parameter changes.

How can I do it? Do you have any suggestion?

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If the two time series were recorded at the same moments of time (more or less) then vector autoregressions (VAR) is one way of combining them. They allow you to model the two time series as a 2-dimensional process $(X_t, Y_t)$ and check if values $(X_{t-1}, Y_{t-1})$ are predictive of $X_t$ or $Y_t$.

Many tests have been developed for detecting structural changes and/or trends in VAR.

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