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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 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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    $\begingroup$ The question fits here alright, but just FYI: an alternative place to ask this would be Economics Stack Exchange. Where it is best to post it would depend on whether you need statistical expertise or economics expertise more. $\endgroup$ Nov 7, 2020 at 17:15
  • $\begingroup$ Hi! Thanks for the advice, I would like to put here first, if it doesn't satisfactory responses, i'll move it to econ exchange $\endgroup$
    – pkg7724
    Nov 7, 2020 at 17:52

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Hi: One way to think about it is the following: Suppose one has the two cases:

$y_t = y_{t-1} + \epsilon_t $

$y_t = \alpha y_{t-1} + \nu_t $

In the first case, when there's a shock, such as $\epsilon_t$, from $t$ an onwards, it stays in the response forever and never leaves. That's a non-stationary process.

In the second case, (assume $\alpha$ is less than 1.0 ), when there's a shock, such as $\nu_t$, initially it all gets put into the response, $y_t$. But, over time, the effect of the shock at time $t$ dies out because over time, it gets multiplied by higher and higher powers of $\alpha$.

So, maybe the first case somehow applies to GDP but this is just an example of unit-root non-stationarity. There can be other types of processes that are non-stationary which are not due to a unit-root.

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