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I have a set of over 400 days within my time series, my goal is to detect when a particular trend breaks and another one begins. For example, for days 1-30, an ARIMA(0, 1, 1) will be the most appropriate, but from days 30-74 an ARIMA(2, 1, 2) will the best fit.

Is there a way I can check something like this? My understanding was the ACF function but I'm a bit confused about this now too. Could someone point me to some resources that may explain?

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If you google "change point analysis" you will find tons of pointers.

It is not clear to me from your question whether you want to check for a change at a suspected, fixed point in time or rather you want to screen your time series for possible changes at some (unspecified) point of time. In the first case you might search for "intervention analysis" or "interrupted time series" (which seems to be a popular name for the same thing in medical and biological literature).

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  • $\begingroup$ Hi Tusell, thank you so much for your suggestions. Could you point me to some notes in the 2nd case? Thanks! $\endgroup$ – Wallace Mar 1 at 23:05
  • $\begingroup$ Well, it is a very broad question, much depends on the problem at hand. Besides searching for "change point analysis" you migh also search "cusum tests" and "structural change". You have pages in the Wikipedia for both topics, providing some explanation and links. $\endgroup$ – F. Tusell Mar 2 at 8:46

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