Minimally Conditioned Likelihood for a Nonstationary State Space Model

José Casals (), Sonia Sotoca and Miguel Jerez
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José Casals: Departamento de Fundamentos del Análisis Económico II. Facultad de Ciencias Económicas. Campus de Somosaguas. 28223 Madrid (SPAIN)., https://www.ucm.es/fundamentos-analisis-economico2
Sonia Sotoca: Departamento de Fundamentos del Análisis Económico II. Facultad de Ciencias Económicas. Campus de Somosaguas. 28223 Madrid (SPAIN)., https://www.ucm.es/fundamentos-analisis-economico2

No 2012-04, Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

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.

Keywords: State-space models; Conditional likelihood; Diffuse likelihood; Diffuse initial conditions; Kalman filter; Nonstationarity. (search for similar items in EconPapers)
JEL-codes: C10 C32 C51 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2012
New Economics Papers: this item is included in nep-ecm and nep-ets
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