Non-Stationarity Effects in Causal Sales Forecasting Models

Abstract

One fundamental assumption of classical econometrics that is gaining a lot of attention in econometric modeling is that of stationarity of variables used to specify a regression model. We analyze some of the benefits and drawbacks in applying econometric models of nonstationary behavior to forecasts involving marketing variables. We use standard residual-based unit root and cointegration tests to identify non-stationary variables in the sales and marketing data of two CPG brands and any potential long-run equilibrium. The out-of-sample forecast Mean Absolute Percent Errors (MAPE) from single-equation causal forecast models of sales volume for the brands, with the identified non-stationary regressors is compared to that from benchmark univariate models, to gauge the effect of nonstationarity on forecast quality. The model is then re-specified after appropriately stationarizing these models. The forecasts from the stationarized models are compared to the benchmark models to analyze potential improvements in forecast quality.

The results show that it may not be necessary to difference nonstationary, non-cointegrating regressors, when the dependent variable is stationary, and when the dependent variable is nonstationary, it might be possible to obtain a stable regression model with levels variable by using an autoregressive error model.

Keywords: Forecasting, Nonstationarity, Cointegration, Marketing, Unit Root

JEL Classification: C53