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When dealing with non-stationary time series (for instance, in auto-correlation analysis), differencing (computing absolute differences between consecutive samples/observations) is often regarded as the simplest method of de-trending the data.

In theory, the first derivative (similar to what is obtained when computing the gradient using central differences) should also remove any underlying trends in the time series. What would be the advantages/drawbacks of using one over the other?

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  • $\begingroup$ Definitions can vary but time series are usually taken to be discretely sampled, so there is no derivative. Are you suggesting a continuous time series, or a continuous time approximating model? Or just a centered difference? The first obvious issue with the latter is that it then depends on future data. Another is that the random walk is a classic model for which the usual difference yields a nice IID sequence, but the centered difference would give an MA(1) process instead, so is less "natural" in that sense. $\endgroup$
    – Chris Haug
    Commented May 31, 2023 at 1:18
  • $\begingroup$ I was referring to the latter, I'm getting vastly different ACF/PACF plots in both case got curious since I was expecting very similar results. But judging by your comment I guess it's normal. $\endgroup$
    – joaocandre
    Commented May 31, 2023 at 14:19

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