Casals Carro, JoséJerez Méndez, MiguelSotoca López, Sonia2023-06-202023-06-202006Akaike, H. (1973). “Information Theory and an Extension of the Maximum Likelihood Principle,” in B.N. Petrov and F. Csaki, Proc. 2nd International Symposium on Information Theory, (eds.), 267-281, Akademia Kiado, Budapest. Bhattacharyya, M.N. (1982). “Lydia Pinkham Data Remodelled,” Journal of Time Series Analysis, 3, 81-102. Box, G.E.P. and G. Tiao (1975). “Intervention Analysis with Applications to Economic and Environmental Problems,” Journal of the American Statistical Association, 70, 70-79. Casals, J., S. Sotoca and M. Jerez (1999). “A Fast and Stable Method to Compute the Likelihood of Time Invariant State-Space Models,” Economics Letters, 65, 329-337. Casals, J., M. Jerez and S. Sotoca (2000). “Exact Smoothing for Stationary and Nonstationary Time Series,” International Journal of Forecasting, 16, 1, 59-69. Casals, J., M. Jerez and S. Sotoca (2002), “An Exact Multivariate Model-based Structural Decomposition,” Journal of the American Statistical Association, 97, 458, 553-564. De Jong, P. (1988), “The Likelihood for a State Space Model,” Biometrika, 75, 165-169. De Jong, P. and S. Chu-Chun-Lin (1994), “Stationary and Non-Stationary State Space Models,” Journal of Time Series Analysis, 15, 151-166. De Jong, P. and J.R. Penzer (1998). “Diagnosing shocks in time series,” Journal of the American Statistical Association, 93, 796-806. Golub, G.H., and C.F. Van Loan (1996). Matrix Computations. Baltimore: John Hopkins University Press. Houston, F.S. and D.L. Weiss (1975). “Cumulative Advertising Effects: The Role of Serial Correlation,” Decision Sciences, 6, 471-481. Kim, Jae H. (2005). “Investigating the advertising-sales relationship in the Lydia Pinkham data: a bootstrap approach.” Applied Economics, 37, 3, 347 – 354. Ljung, G. and G.E.P. Box (1978). “On a Measure of Lack of Fit in Time Series Models,” Biometrika, 67, 297-303. Palda, K. (1964). The Measurement of Cumulative Advertising Effects, Prentice-Hall, Englewood Cliffs (NJ). Petkov, P. Hr., N.D. Christov and M.M. Konstantinov (1991). Computational Methods for Linear Control Systems, Prentice-Hall, Englewood Cliffs, New Jersey. Rosenbrock, M.M. (1970). State-Space and Multivariable Theory, John Wiley, New York. Schwarz, G. (1978). “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461-464. Smith, A. Naik, P. A. and C. Tsai (2006). “Markov-switching model selection using Kullback–Leibler divergence,” Journal of Econometrics, 134, 2, 553-577. Terceiro, J. (1990). Estimation of Dynamic Econometric Models with Errors in Variables, Springer-Verlag, Berlin. Van Overschee, P. and B. De Moor (1994). “N4SID*: Subspace algorithms for the identification of combined deterministic-stochastic systems,” Automatica, 30, 75-93. Wei, W.S. (1994). Time Series Analysis: Univariate and Multivariate Methods, AddisonWesley, New York.https://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.engtechnical reporthttps://www.ucm.es/icaeopen accessC32C53State-spaceSignal extractionTime series decompositionSeasonal adjustmentAdvertisingLydia PinkhamEconometría (Economía)5302 Econometría