A study of ‘spurious regression’ and model discrimination in the generalized bass model

Abstract

Although opinions among time series econometricians vary concerning whether the variables in linear regression models need to be stationary, the majority view is that stationary variables are desirable, if not required, because of the dangers of “spurious regression,” (Enders, 1985). Trending, but independent, variables will likely be significantly correlated when combined in a regression analysis. The issue of “spurious regression” and the appropriate manner of including explanatory variables in nonlinear models has not been extensively examined. In this study we examine the issue of model discrimination and “spurious regression” between two nonlinear diffusion models. We use the Generalized Bass Model (GBM) proposed by Bass, Krishnan and Jain (1994) where explanatory variables are included as percentage changes and as logarithms in comparison with the Cox (1972) proportional hazard model with non-stationary variables included as levels. We use simulations to analyze estimation properties and model discrimination issues for the two models.