Canonical Correlation Analysis and Wiener-Granger Causality Tests: Useful Tools for the Specification of VAR Models

Abstract

Dynamic multivariate models have become popular in analyzing the behavior of competitive marketing systems because they are capable of incorporating all the relationships in a competitive marketing environment. In this paper we consider VAR models, the most frequently used dynamic multivariate models. The drawback of VAR models is that a large number of parameters have to be estimated. The problem has been addressed in several articles and the usual solution is to treat only the variables of interest as endogenous while the other variables are usually included exogenously without dynamic effects. This treatment imposes restrictions on the marketing system, which requires preliminary analysis. We propose to use canonical correlation for this purpose. Canonical correlation analysis and its associated Wiener-Granger causality testing based on the canonical correlation coefficients are useful tools to test the existence of structural relationships between (lagged) consumer response and (lagged) marketing instruments. The tools are applied on data of market shares and marketing instruments in a market of a frequently purchased consumer goods.