I know that for univariate framework, a typical process to deal with seasonality is :
- correct (for instance, withdraw seasonal factors)
- re-seasonalize the forecasted series (for instance, incorporate seasonal factors back)
What would be the equivalent of such a pattern for VECM ?
The following crossvalidated thread points out that seasonality can be "handled [...] outside of the model (by seasonally adjusting the series before fitting a VAR)". But the precise steps are fuzzy to me.
Let's say $Y$ is my $I(1)$ target variable for VECM and I go :
- check if $Y$ seasonal
- correct with seasonal factors
- Engle-Granger test and find my cointegrating vector
- Forecast Long-Term relationship
- Apply seasonal factors back to re-seasonalize the forecast of $Y$
- Find the rest of VECM ($\Delta Y = ...$ & short-term)
- Forecast short-term relationship and final equation
Is this process correct ?
And what about the case where there is seasonality in the predictors too ?
Let's say, we have seasonality for some of the variables in $ X \;=\; (\;X_1,\;...,\;Xn\;) $ where $X$ is the cointegrating vector. And we come to step 5.
How am I supposed to seasonalize back the forecast ?