Minimally Conditioned Likelihood for a Nonstationary State Space Model

  1. Casals Carro, José
  2. Sotoca López, Sonia
  3. Jerez Méndez, Miguel
Revista:
Documentos de Trabajo (ICAE)

ISSN: 2341-2356

Año de publicación: 2012

Número: 4

Páginas: 1-34

Tipo: Documento de Trabajo

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Otras publicaciones en: Documentos de Trabajo (ICAE)

Resumen

Computing the gaussian likelihood for a nonstationary state-space model is a difficult problem which has been tackled by the literature using two main strategies: data transformation and diffuse likelihood. The data transformation approach is cumbersome, as it requires nonstandard filtering. On the other hand, in some nontrivial cases the diffuse likelihood value depends on the scale of the diffuse states, so one can obtain different likelihood values corresponding to different observationally equivalent models. In this paper we discuss the properties of the minimally-conditioned likelihood function, as well as two efficient methods to compute its terms with computational advantages for specific models. Three convenient features of the minimally-conditioned likelihood are: (a) it can be computed with standard Kalman filters, (b) it is scale-free, and (c) its values are coherent with those resulting from differencing, being this the most popular approach to deal with nonstationary data.

Referencias bibliográficas

  • Ansley, C.F. and Kohn, R. (1990). “Filtering and Smoothing in State Space Models with Partially Diffuse Initial Conditions,” Journal Time Series Analysis 11, 275-93.
  • Ansley, C.F. and R. Kohn (1985). “Estimation, Filtering and Smoothing in State Space Models with Incompletely Specified Initial Conditions,” Annals of Statistics 13, 1286-1316.
  • Bell, W., and Hillmer, S. C. (1991). “Initializing the Kalman Filter for Nonstationary Time Series Models,” Journal of Time Series Analysis, 12, 4, 283-300.
  • Box, G.E.P.; G. M. Jenkins y G. C. Reinsel (2008). Time Series Analysis: Forecasting and Control, Wiley, New York.
  • 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., 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.
  • De Jong, P and S. Chu-Chun-Lin (1994). “Fast Likelihood Evaluation and Prediction for Nonstationary State Space Models,” Biometrika, 81, 133-142.
  • De Jong, P. (1988). “The Likelihood for a State Space Model,” Biometrika 75, 1, 165- 169.
  • De Jong, P. (1991). “The Diffuse Kalman Filter,” Annals of Statistics 19, 1073-1083.
  • Francke, M.K., S. J. Koopman and A. de Vos (2010). “Likelihood Functions for State Space Models with Diffuse Initial Conditions,” Journal of Time Series Analysis, 31, 6, 407-414.
  • Gomez, V. and Maravall, A. (1994). “Estimation, Prediction and Interpolation for Nonstationary Series with the Kalman Filter,” Journal of the American Statistical Association, 89, 611-624.
  • Gomez, V., Maravall, A., and D. Peña, (1999). “Missing Observations in ARIMA Models: Skipping Approach versus Additive Outlier Approach,” Journal of Econometrics, 88, 2, 341-363.
  • Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, Cambridge (UK).
  • Kohn, R. and Ansley, C.F. (1986). “Estimation, Prediction, and Interpolation for ARIMA Models with Missing Data,” Journal of the American Statistical Association, 81, 751-761.
  • Koopman, S.J. (1997). “Exact Initial Kalman Filtering and Smoothing for NonStationary Time Series Models,” Journal of the American Statistical Association, 92, 440, 1630-1638.
  • Mauricio, A. (2006). “Exact Maximum Likelihood Estimation of Partially Nonstationary Vector ARMA Models,” Computational Statistics and Data Analysis 50, 12, 3644-3662.
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