I am using ccf on two univariate time series to find out which variable is leading and which is lagging. My result is something like shown in the plot enter image description here

Can I really tell anything from this plot? Does it mean that x is both leading and lagging y?

The ACF value drops when the lag reaches 0 but still exceeds the boundary.

edit: Attached you find both timeseries plotted: enter image description here

enter image description here

  • 1
    $\begingroup$ Did you prewhiten? $\endgroup$
    – Glen_b
    Commented Aug 24, 2020 at 10:56
  • $\begingroup$ I suspect non-stationairy time series. Can you plot both time series? $\endgroup$
    – Ruben
    Commented Aug 24, 2020 at 13:21
  • $\begingroup$ I did not prewhiten the timeseries before. @Ruben I attached both timeseries. Both are the longterm trend components without seasonal changes. $\endgroup$
    – laura
    Commented Aug 26, 2020 at 9:24

1 Answer 1


To have a valid interpretation of the cross correlation function, time series need to be wide sense stationary. (https://en.wikipedia.org/wiki/Cross-correlation#Cross-correlation_function) Looking at the graphs, both of your time series are not stationary. So it is not ok to interpret this ccf graph.

You can still examine the correlation between these two time series, by checking if the differenced time series are stationary and computing the correlation of the differenced time series in case of stationarity.


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