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

Author

Listed:
  • José Casals Carro

    (Universidad Complutense de Madrid. Departamento de Fundamentos del Análisis Económico II.)

  • Miguel Jerez Méndez

    (Universidad Complutense de Madrid. Departamento de Fundamentos del Análisis Económico II.)

  • Sonia Sotoca López

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.

Suggested Citation

  • José Casals Carro & Miguel Jerez Méndez & Sonia Sotoca López, 2006. "Decomposition of state-space Model with inputs: The theory and an application to estimate the ROI of advertising," Documentos de Trabajo del ICAE 0602, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:0602
    as

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    File URL: https://eprints.ucm.es/id/eprint/7910/1/0602.pdf
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    References listed on IDEAS

    as
    1. Casals, Jose & Jerez, Miguel & Sotoca, Sonia, 2000. "Exact smoothing for stationary and non-stationary time series," International Journal of Forecasting, Elsevier, vol. 16(1), pages 59-69.
    2. M. N. Bhattacharyya, 1982. "Lydia Pinkham Data Remodelled," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(2), pages 81-102, March.
    3. Pidt de Jong & Singfat Chu‐Chun‐Lin, 1994. "Stationary And Non‐Stationary State Space Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 151-166, March.
    4. Jae Kim, 2005. "Investigating the advertising-sales relationship in the Lydia Pinkham data: a bootstrap approach," Applied Economics, Taylor & Francis Journals, vol. 37(3), pages 347-354.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    State-space; Signal extraction; Time series decomposition; Seasonal adjustment; Advertising; Lydia Pinkham;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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