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!


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).

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.