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I am wanting to apply a changepoint detection method to a timeseries but an assumption is that the data points are independent from each other.

I was wondering if there is a way to check this when the data might be non-stationary? The reason I ask is that when I have done correlation plots or the Ljung-Box test on synthetic non-stationary timeseries, they show up sometimes as showing correlation even thought the samples are independent from each other.

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  • $\begingroup$ This may depend on the type of nonstationarity. Is it a unit root? Nonconstant variance? Something else? $\endgroup$
    – Richard Hardy
    Commented Feb 10, 2021 at 19:04
  • $\begingroup$ @RichardHardy Nonconstant variance and potentially nonconstant mean $\endgroup$
    – math111
    Commented Feb 10, 2021 at 20:12

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This is an interesting question. You cannot check this assumption before analysis because the changepoints make the data non-stationary and so standard stationary methods for assessing independence/correlation are no longer valid.

The best way is to perform a changepoint analysis and then look at the residuals (remove the time varying mean/variance) to see if they are independent/correlated.

You can find an example of how to checking the assumptions of a changepoint analysis here, pg 44 onwards. The example given there is a change in mean but the approach generalizes to other changepoint models.

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  • $\begingroup$ Thank you. So suppose we have a changing variance and mean, would I centre the data and then normalise by the standard deviation? $\endgroup$
    – math111
    Commented Feb 11, 2021 at 16:21
  • $\begingroup$ Yes, you subtract the fitted mean for each segment and then divide by the segment standard deviation. This should then be the error distribution of the original model, often Normal(0,1). $\endgroup$
    – adunaic
    Commented Feb 12, 2021 at 17:19

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