Abstract
Multivariate structural models are defined in a way similar to that of univariate structural models, described in Sect. 4.1. For example, let the stochastic vector Y t satisfy Y t = P t + S t + I t, where P t is the trend, S t is the seasonal, and I t is the irregular component.
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References
Akaike, H. (1974). Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes. Annals of the Institute of Statistical Mathematics,26, 363–387.
Cleveland, W. P., & Tiao, G. C. (1976). Decomposition of seasonal time series: A model for the X-11 program. Journal of the American Statistical Association,71, 581–587.
Creal, D., Koopman, S. J., & Zivot, E. (2010). Extracting a robust US business cycle using a time–varying multivariate model–based bandpass filter. Journal of Applied Econometrics,25, 695–719.
Doménech, R., & Gómez, V. (2006). Estimating potential output, core inflation, and the NAIRU as latent variables. Journal of Business and Economic Statistics,24, 354–365.
Gómez, V. (2001). The use of butterworth filters for trend and cycle estimation in economic time series. Journal of Business and Economic Statistics,19, 365–373.
Gómez, V. (2016). Multivariate time series models with linear state space structure. New York: Springer.
Gómez, V., & Aparicio-Pérez, F. (2009). A new state-space methodology to disaggregate multivariate time series. Journal of Time Series Analysis,30, 97–124.
Gómez, V., & Maravall, A. (1994). Estimation, prediction, and interpolation for nonstationary series with the Kalman filter. Journal of the American Statistical Association,89, 611–624.
Gómez, V., & Maravall, A. (2001). Programs TRAMO and SEATS, instructions for the user (Beta Version: June 1997) (Working Paper No. 97001). Dirección General De Presupuestos, Ministry of Finance, Madrid, Spain.
Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge University Press.
Mariano, R. S., & Murasawa, Y. (2003). A new coincident index of business cycles based on monthly and quarterly series. Journal of Applied Econometrics,18, 427–443.
Valle e Azevedo, J., Koopman, S. J., & Rua, A. (2006). Tracking the business cycle of the euro area: A multivariate model–based bandpass filter. Journal of Business and Economic Statistics,24, 278–290.
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Gómez, V. (2019). Multivariate Structural Models. In: Linear Time Series with MATLAB and OCTAVE. Statistics and Computing. Springer, Cham. https://doi.org/10.1007/978-3-030-20790-8_7
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DOI: https://doi.org/10.1007/978-3-030-20790-8_7
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