I am trying to fit a Vector Autoregression model to forecast GDP growth Rate.
I have 2 series, monthly GDP growth rate and a monthly economic indicator. For the monthly GDP growth rate, the latest growth rate I can use is from the previous quarter. For the monthly economic indicator, I am able to get it near real time.
Meaning, to forecast 2016-Apr GDP growth, I can only use 2016-Mar or earlier GDP data and 2016-Apr or earlier economic indicator data. Likewise, to forecast 2016-May GDP growth, I can only use 2016-Mar or earlier GDP data and 2016-May or earlier economic indicator data.
As the latest economic indicator contains a lot of information on the GDP growth, I would like to include it in the VAR model.
My question is, is it okay to fit the VAR model in such a way where the 2 series came from different time interval (i.e. fit model with GDP data from t-3 to t, and economic indicator data from t-2 to t+1)?
And is it appropriate to forecast GDP by simply using 1-step ahead forecast?
Using the above model specification, I am able to get decent forecast performance. I am more concern if I am using VAR model inappropriately or violated anything statistically.