0
$\begingroup$

what is general forecasting equation for sARIMA(p,d,q)(P,D,Q)s.?

I wrote this equation, can someone confirm if it is a correct one?

$\overline{y}_{t+m}=\frac{ (\varphi_{1}y_{t} + \varphi_{2}y_{t-1}+...+ \varphi_{p}y_{t-p+m})(\phi_{1}y_{t} + \phi_{2}y_{t-s}+...+ \phi_{P}y_{t-P+m})}{(\theta_{1}e_{t}-\theta_{2}e_{t-1}-...-\theta_{q}e_{t-q+m})(\Theta_{1}e_{t}-\Theta_{2}e_{t-s}-...-\Theta_{Q}e_{t-Q+m})}$

If not, can someone correct it?

I need it in a form $\overline{y}_{t+m}= ....$

Thank you in advance!

Improve this question
$\endgroup$
2
  • $\begingroup$ 1) It seems that you are trying to write the infinite moving-average represenation of the ARIMA model, in which case the lag operator should be applied to the innovations $e_t$ not to the series $y_t$. A more natural equation for the forecasts is the equation of the ARIMA model itself; simply move the indices $m$ observations forward, no need for the fraction of polynomials; it will look more like $y_{t+1} = \phi y_t + \epsilon_t + \theta \epsilon_{t-1}$. 2) You are not accounting for $d$ and $D$. 3) The indices should go $t+m-1,t+m-2,...,t+m-p$ and for the seasonal $t+m-s,t+m-2s,...,t+m-Ps$. $\endgroup$
    – javlacalle
    Commented Dec 11, 2014 at 19:05
  • $\begingroup$ Yo may want to add the tag self-study to your question. $\endgroup$
    – javlacalle
    Commented Dec 11, 2014 at 19:06

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.