I am trying to understand overdifferencing, if I were to first difference a stationary time series, would that time series remain stationary? Would it become white noise? Does it actually make the time series less stable?
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A recent thread on overdifferencing appears at http://stats.stackexchange.com/questions/250728. I believe it might answer all your questions. – whuber Dec 15 '16 at 00:27
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@whuber Saw your answer to the referenced question. Did you get the bounty? The question was about iid variables. It is a special case of an uncorrelated time series that is stationary. My intuitive thinking is that it adds spurious trends to the time series and that could explain the instability . For the OPs benefit I do not think the differenced series would look anything like white noise. – Michael R. Chernick Dec 15 '16 at 00:37
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@Michael: I think you're right. Look at it in reverse. If a differenced series were white noise, then that original series would be integrated white noise--that is, Brownian Motion--which obviously is not stationary. BTW, that bounty lasts another 5 days. If I were the OP I wouldn't award it until the last moment, because it might continue attracting attention and bring in additional replies. – whuber Dec 15 '16 at 00:44
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2Does this answer your question? High autocorrelation when taking the L-th order of difference of a sequence of independent random numbers – kjetil b halvorsen Oct 04 '20 at 01:38