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As i just read in a time series book that a particular GDP data under consideration is non-stationary verified through various tests. From non-stationarity definition this means that the process has infinite memory and also specifically 'persistence of random shocks' i.e. shocks do not die away. But can someone enlighten me how I can think this intuitively or practically like say during recession GDP sinks but it eventually recovers from that period to new highs, so how does this infinite memory of old shocks or significant change in value affects the random walk of GDP over such long period of time or say in coming period after event has been happened more than 2-3 decades ago?

Please bear with the question, studying into basic intro time series subject. Thanks :)

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  • $\begingroup$ I think you made some mistake since you say: "From stationarity definition this means that the process has infinite memory" but it should be non-stationarity definition because stationary data do not have infinite memeroy $\endgroup$
    – 1muflon1 ♦
    Nov 7, 2020 at 18:16
  • $\begingroup$ Also does this answer your problem? $\endgroup$
    – 1muflon1 ♦
    Nov 7, 2020 at 18:48
  • $\begingroup$ It is important to recognise that underlying 'stationarity' is a concept known as 'weak dependence'. To begin, 'stationarity' implies that the underlying statistical processes for today and tomorrow are the same (time-invariant). Yet, by comparison, if there is a shock, and this shock (transforms the underlying processes for the time after tomorrow, then the process is non-stationary. If by comparison, the shock is less significant, the process will exhibit stationarity/mean-reversion. And typically, this is upheld when a time series is weakly dependent (shocks quickly die) $\endgroup$
    – EB3112
    Nov 7, 2020 at 22:22

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