Decomposition of state-space Model with inputs: The theory and an application to estimate the ROI of advertising

José Casals Carro, Miguel Jerez and Sonia Sotoca López
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José Casals Carro: Universidad Complutense de Madrid. Departamento de Fundamentos del Análisis Económico II.

Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

Abstract: This paper shows how to compute the in-sample effect of exogenous inputs on the endogenous variables in any linear model written in state-space form. Estimating this component may be, either interesting by itself, or a previous step before decomposing a time series into trend, cycle, seasonal and error components. The practical application and usefulness of this method is illustrated by estimating the effect of advertising on monthly sales of the Lydia Pinkham vegetable compound.

Keywords: State-space; Signal extraction; Time series decomposition; Seasonal adjustment; Advertising; Lydia Pinkham (search for similar items in EconPapers)
JEL-codes: C32 C53 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2006
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