Template-type: ReDIF-Paper 1.0
Author-Name: José Casals
Author-Email: jcasalsc@cajamadrid.es
Author-Workplace-Name: Departamento de Fundamentos del Análisis Económico II. Facultad de Ciencias Económicas. Campus
de Somosaguas. 28223 Madrid (SPAIN).
Author-Workplace-Homepage: https://www.ucm.es/fundamentos-analisis-economico2
Author-Name: Sonia Sotoca
Author-Workplace-Name: Departamento de Fundamentos del Análisis Económico II. Facultad de Ciencias Económicas. Campus
de Somosaguas. 28223 Madrid (SPAIN).
Author-Workplace-Homepage: https://www.ucm.es/fundamentos-analisis-economico2
Author-Name: Miguel Jerez
Author-Email: mjerez@ccee.ucm.es
Author-Person: pje52 
Author-Workplace-Name: Departamento de Fundamentos del Análisis Económico II. Facultad de Ciencias Económicas. Campus
de Somosaguas. 28223 Madrid (SPAIN).
Author-Workplace-Homepage: https://www.ucm.es/fundamentos-analisis-economico2
Title: Minimally Conditioned Likelihood for a Nonstationary State Space Model
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.
Classification-JEL: C32, C51, C10.
Keywords: State-space models, Conditional likelihood, Diffuse likelihood, Diffuse initial conditions, Kalman filter, 
	Nonstationarity.
Length: 34 pages 
Creation-Date: 2012 
Number: 2012-04 
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1204.txt
File-URL: https://eprints.ucm.es/id/eprint/14621/1/1203.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1204