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I am very new to this topic. From what I understand, time series prediction with ARIMA requires that the series be series. So there is no seasonality, and no trend. In my limited understanding, this means that there is only "non-systematic" data in the series. Which, again according to my limited understanding, is random. Given this, what is there to predict, considering we have only the random component of the time series left?

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    $\begingroup$ Your understanding is incorrect, the remainder term is just not random component it includes both signal which is also ARMA component and the rest is noise. ARIMA specifically addresses the remainder competent and extracts signal from it and whatever is left over is the noise or what you call random component. $\endgroup$
    – forecaster
    Jun 28 '19 at 17:20
  • $\begingroup$ @forecaster - According to a few websites, the components of a time series are trend, seasonal, and irregular ("random"). So which is ARIMA tracking after removing trend and seasonal? (example: abs.gov.au/websitedbs/D3310114.nsf/home/…) $\endgroup$
    – HorseHair
    Jun 29 '19 at 16:38

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