Advanced Search
MyIDEAS: Login

Likelihood Functions for State Space Models with Diffuse Initial Conditions

Contents:

Author Info

  • Marc K. Francke

    ()
    (Vrije Universiteit Amsterdam)

  • Siem Jan Koopman

    ()
    (Vrije Universiteit Amsterdam)

  • Aart de Vos

    ()
    (Vrije Universiteit Amsterdam)

Abstract

State space models with nonstationary processes and fixed regression effects require a state vector with diffuse initial conditions. Different likelihood functions can be adopted for the estimation of parameters in time series models with diffuse initial conditions. In this paper we consider profile, diffuse and marginal likelihood functions. The marginal likelihood is defined as the likelihood function of a transformation of the data vector. The transformation is not unique. The diffuse likelihood is a marginal likelihood for a specific data transformation that may depend on parameters. Therefore, the diffuse likelihood can not be used generally for parameter estimation. Our newly proposed marginal likelihood function is based on an orthonormal transformation that does not depend on parameters. Likelihood functions for state space models are evaluated using the Kalman filter. The diffuse Kalman filter is specifically designed for computing the diffuse likelihood function. We show that a modification of the diffuse Kalman filter is needed for the evaluation of our proposed marginal likelihood function. Diffuse and marginal likelihood functions have better small sample properties compared to the profile likelihood function for the estimation of parameters in linear time series models. The results in our paper confirm the earlier findings and show that the diffuse likelihood function is not appropriate for a range of state space model specifications.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://papers.tinbergen.nl/08040.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-040/4.

as in new window
Length:
Date of creation: 14 Apr 2008
Date of revision:
Handle: RePEc:dgr:uvatin:20080040

Contact details of provider:
Web page: http://www.tinbergen.nl

Related research

Keywords: Diffuse likelihood; Kalman filter; Marginal likelihood; Multivariate time series models; Profile likelihood;

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Kuo, Biing-Shen, 1999. "Asymptotics Of Ml Estimator For Regression Models With A Stochastic Trend Component," Econometric Theory, Cambridge University Press, vol. 15(01), pages 24-49, February.
  2. Francke, Marc K. & de Vos, Aart F., 2007. "Marginal likelihood and unit roots," Journal of Econometrics, Elsevier, vol. 137(2), pages 708-728, April.
  3. Rahman, Shahidur & King, Maxwell L., 1997. "Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters," Journal of Econometrics, Elsevier, vol. 82(1), pages 81-106.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Luati, Alessandra & Proietti, Tommaso, 2012. "Maximum likelihood estimation of time series models: the Kalman filter and beyond," Working Papers 02 BAWP, University of Sydney Business School, Discipline of Business Analytics.
  2. José Casals & Sonia Sotoca & Miguel Jerez, 2012. "Minimally Conditioned Likelihood for a Nonstationary State Space Model," Documentos del Instituto Complutense de Análisis Económico 2012-04, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
  3. Søren Johansen & Marco Riani & Anthony C. Atkinson, 2012. "The Selection of ARIMA Models with or without Regressors," Discussion Papers 12-17, University of Copenhagen. Department of Economics.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:dgr:uvatin:20080040. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Antoine Maartens (+31 626 - 160 892)).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.