I am facing a situation where I am given a relatively short time series (in the worst-case scenario it may have up to 15 observations). During the time series we modify one external factor that we believe has an impact on the level of the measured variable. For instance, imagine that we sample heart rate of a person and, as we sample it - we ask them to do some push-ups. We basically want to quantify the level of the change that we (potentially!) introduced with that external factor. I may add that we know when the change was introduced, so we know when to split the time series into pre- and post-periods. Is there a way to do that statistically given the short nature of the time series?

A plot to ease the understanding: enter image description here

We want to compare the blue segment with the red segment. Please mind that, contrarily to the time series that is depicted here, the change may not be that pronounced or there may be no change at all!

My initial ideas were:

  1. Run linear regression on both sub-samples and compare the slopes and biases of the results. I do not know what test to use - will ANOVA be adequate given the time aspect?
  2. Use Granger causality test to see if the series of 0s and 1s is useful in predicting the time series of our interest.
  3. Apply one of the breakpoint (change point) detection tests, but I am not sure if the time series is not too short.

Has anyone had similar problem?



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