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I have an ARIMA(4,0,2) model that works well for 168-differenced data, that is, I fitted it to $Y_t-Y_{t-168}$.

Based on this, would it be a good idea to try to fit a Seasonal ARIMA(4,0,2)(0,1,0)[168] or a SARIMA(4,0,2)(0,1,1)[168]?

What would be a good way to decide the order of the polynomial in $B^{168}$ in front of the white noise terms?

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  • $\begingroup$ I'm curious what type of business or natural time series has a 168 periodicity? $\endgroup$
    – Skander H.
    Commented May 11, 2019 at 3:16
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    $\begingroup$ @Skander H. It’s hourly data of energy consumption with daily and weekly periodicity $\endgroup$
    – John Cataldo
    Commented May 11, 2019 at 7:24

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The first is the obvious candidate, since it's implied by the differencing (i.e. if you difference that first SARIMA you get the initial ARIMA model - with a zero mean).

However, that doesn't mean that the model with more parameters won't be noticeably a better model -- there's to little information here to judge what the circumstances really are.

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  • $\begingroup$ I just spotted a mangled phrase (I broke it during the initial edit), which was quite misleading. Now fixed. $\endgroup$
    – Glen_b
    Commented May 12, 2019 at 2:21

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