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I've decomposed my data to get rid of the seasonality. Now I want to use the arima function to fit an ARMA(p,q) model.

Do I fit the model to the "random" component of the decomposition? That seems odd to me, as surely it's just white noise?

Or should I fit the model to the "trend" component?

Thanks for your help!

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You should fit ARIMA to the remainder. Indeed, if your trend is linear, it's completely described by a fomula like $at+b$ where $a$ and $b$ can be estimated by least squares (and this doesn't contain AR/MA parts).

Moreover, ARIMA on the remainder is precisely useful when residuals $\eta_t$ of the linear regression $X_t = at+b+\eta_t$ aren't pure white noise and do contain some non-trivial autocorrelation (which can be modelled by ARIMA).

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