Decomposition of State-Space Model with InputsThe Theory and an Applicatuion to Estimate the ROI of Advertising

1. Casals Carro, José
2. Jerez Méndez, Miguel
3. Sotoca López, Sonia

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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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