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Minimally Conditioned Likelihood for a Nonstationary State Space Model

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Abstract

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.

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Paper provided by Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico in its series Documentos de Trabajo del ICAE with number 2012-04.

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Length: 34 pages
Date of creation: 2012
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Handle: RePEc:ucm:doicae:1204

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Related research

Keywords: State-space models; Conditional likelihood; Diffuse likelihood; Diffuse initial conditions; Kalman filter; Nonstationarity.;

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  1. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
  2. Casals, Jose & Jerez, Miguel & Sotoca, Sonia, 2000. "Exact smoothing for stationary and non-stationary time series," International Journal of Forecasting, Elsevier, vol. 16(1), pages 59-69.
  3. Marc K. Francke & Siem Jan Koopman & Aart de Vos, 2008. "Likelihood Functions for State Space Models with Diffuse Initial Conditions," Tinbergen Institute Discussion Papers 08-040/4, Tinbergen Institute.
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