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

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Author Info
José Casals Carro
Miguel Jerez Méndez () (Universidad Complutense de Madrid. Departamento de Fundamentos del Análisis Económico II.)
Sonia Sotoca López

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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.

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File URL: http://eprints.ucm.es/7910/
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Publisher Info
Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales in its series Documentos del Instituto Complutense de Análisis Económico with number 0602.

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Date of creation: 2006
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Handle: RePEc:ucm:doicae:0602

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  1. Casals, Jose & Sotoca, Sonia & Jerez, Miguel, 1999. "A fast and stable method to compute the likelihood of time invariant state-space models," Economics Letters, Elsevier, vol. 65(3), pages 329-337, December. [Downloadable!] (restricted)
  2. Kristian S. Palda, 1964. "The Measurement of Cumulative Advertising Effects," Journal of Business, University of Chicago Press, vol. 38, pages 162. [Downloadable!]
  3. Jae H. Kim, 2005. "Investigating the advertising-sales relationship in the Lydia Pinkham data: a bootstrap approach," Applied Economics, Taylor and Francis Journals, vol. 37(3), pages 347-354, February. [Downloadable!] (restricted)
  4. Casals J. & Jerez M. & Sotoca S., 2002. "An Exact Multivariate Model-Based Structural Decomposition," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 553-564, June. [Downloadable!] (restricted)
  5. Smith, Aaron & Naik, Prasad A. & Tsai, Chih-Ling, 2006. "Markov-switching model selection using Kullback-Leibler divergence," Journal of Econometrics, Elsevier, vol. 134(2), pages 553-577, October. [Downloadable!] (restricted)
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