Beautifully explained.

I’d like to know which regression technique is an appropriate one to use to find out drivers of the sales forecast. Because the macroeconomic variables are too less in number ( let’s say 10 variables with quarter wise info of 3 years) and runnign an OLS is not feasible.

Looking forward to a response.

Thanks

Regression was used originally developed for cross sectional data and then subsequently abused in time series. The approach taken to identify the model using an “experiment” is one way to go and is how things had to be done before the power of modern day computing, but using a “data driven” approach can be done by letting the “data speak”(Box-Jenkins quote) using statistics to generate the hypothesis(“hypothesis generation”). Box-Jenkins described how to do this in their landmark book “Forecasting and Control” where the causals have ARIMA models built for them and the residuals are then correlated with the X’s to IDENTIFY the correlation (and lead and lag effects). The four steps they laid out where identification, estimation, diagnostic checking and forecasting.

From the model posted above, there is no ARIMA component stated to capture the inherent quarter to quarter relationship. Not ever model has this, but it’s usually there. There could also be a denominator component(ie decay or lag) on each of the X’s. There was mention of lags being searched for but the model above doesn’t show it. I also heard no discussion on the search for outliers(they always exist, but they are somehow “forgotten” when it comes to causal problems), changes in level, trend, parameters and variance. I did see the mention of variance inflation so I will asssume that was included. As Box-Jenkins said, “All models are wrong, but some are useful”. I would suggest considering investigating (or have Cap-Gemini consider) some of the up-armor modeling I mentioned above.

I am currently doing a PhD on this topic, so I find the problem very interesting as well.

How did you select the variables?