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

Casals Carro, JoséJerez Méndez, MiguelSotoca López, Sonia2023-06-202023-06-202006https://hdl.handle.net/20.500.14352/56636This 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.engDecomposition of state-space Model with inputs: The theory and an application to estimate the ROI of advertisingtechnical reporthttps://www.ucm.es/icaeopen accessC32C53State-spaceSignal extractionTime series decompositionSeasonal adjustmentAdvertisingLydia PinkhamEconometría (Economía)5302 Econometría