Padé Approximation Modelling of an Advertising-Sales Relationship

M. C. Gil-Fariña, C. Gonzalez-Concepcion, C. Pestano-Gabino

Department of Applied Economics, Faculty of Economics and Business Administration, University of La Laguna (ULL), Campus of Guajara, Tenerife, Spain.

DOI: 10.4236/jssm.2010.31011                

Abstract

Forecasting reliable estimates on the future evolution of relevant variables is a main concern if decision makers in a variety of fields are to act with greater assurances. This paper considers a time series modelling method to predict relevant variables taking VARMA and Transfer Function models as its starting point. We make use of the rational Padé-Laurent Approximation, a relevant type of rational approximation in function theory that allows the decision maker to take part in the building of estimates by providing the available information and expectations for the decision variables. This method enhances the study of the dynamic relationship between variables in non-causal terms and allows for an ex ante sensibility analysis, an interesting matter in applied studies. The alternative proposed, however, must adhere to a type of model whose properties are of an asymptotic nature, meaning large chronological data series are required for its efficient application. The method is illustrated through the well-known data series on advertising and sales for the Lydia Pinkham Medicine Company, which has been used by various authors to illustrate their own proposals.

Keywords

Time Series Modelling, Expectations, Economics, Numerical Methods, Padé Approximation

Conflicts of Interest

The authors declare no conflicts of interest.

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