I have the following time series dataset (dependent | independent) :
Sales | Income,Inflation, Interest Rates etc
All of this is dynamic data pertaining to each of 24 months (month:0 to month:24). For 25th month onward I have no data for the independent variables (Income,Inflation, Interest Rates etc), yet I want to be able to predict sales for month:25 +.
I have been trying to figure out models which I can used to implement this scenario including Dynamic Regression and ARMAX/ARIMAX models. However, it seems that to be able to predict sales for the 25th month, i need data for dependent variables (Income,Inflation, Interest Rates etc) for the month (25).
Can I create a model using lagged values of the dependent and independent variables, used together in a regression model? I'm not sure if that makes sense.
This is my first time series model and im not sure if i am on the right track. Please advise.
Best Answer
You could predict the independent variables using separate models or expert forecasts (the latter should be available for variables of such broad interest as
income,inflationandinterest rates). Then you could use them in the fitted ARMAX model to predictsales.Alternatively, you could model the variables together using a vector autoregression (VAR) (or a vector error correction model -- a version of VAR suited for cointegrated variables). This would allow forecasting all of the variables within one model. One-step-ahead forecasts from a VAR are straightforward, while multiple-step-ahead forecasts can be constructed iteratively.
See this answer for a comparison of ARMAX and VAR models.
Yes, you could also do that within an ARMAX or a VAR framework to forecast the dependent variable directly using lags of itself and the other variables. For $h$-step-ahead forecasts you would need to use lags of at least $h$ to enable direct forecasting.