Maximum likelihood estimation for score-driven models

Francisco Blasques; Janneke van Brummelen; Siem Jan Koopman; André Lucas

doi:10.1016/j.jeconom.2021.06.003

Maximum likelihood estimation for score-driven models

Francisco Blasques, Janneke van Brummelen, Siem Jan Koopman^*, André Lucas

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

416 Downloads (Pure)

Abstract

We establish strong consistency and asymptotic normality of the maximum likelihood estimator for stochastic time-varying parameter models driven by the score of the predictive conditional likelihood function. For this purpose, we formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality both under correct specification and misspecification of the model. A detailed illustration is provided for a conditional volatility model with disturbances from the Student's t distribution.

Original language	English
Pages (from-to)	325-346
Number of pages	22
Journal	Journal of Econometrics
Volume	227
Issue number	2
DOIs	https://doi.org/10.1016/j.jeconom.2021.06.003
Publication status	Published - Apr 2022

Bibliographical note

Funding Information:
We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Amsterdam; the ?7th International Conference on Computational and Financial Econometrics?, London; the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation, (DNRF78). An overview of contributions on score-driven models is provided at http://gasmodel.com.

Funding Information:
We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Amsterdam; the ”7th International Conference on Computational and Financial Econometrics”, London; the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005 ) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099 ) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation , ( DNRF78 ). An overview of contributions on score-driven models is provided at http://gasmodel.com .

Publisher Copyright:
© 2021 Elsevier B.V.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

Funding

We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Amsterdam; the ?7th International Conference on Computational and Financial Econometrics?, London; the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation, (DNRF78). An overview of contributions on score-driven models is provided at http://gasmodel.com. We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Amsterdam; the ”7th International Conference on Computational and Financial Econometrics”, London; the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005 ) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099 ) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation , ( DNRF78 ). An overview of contributions on score-driven models is provided at http://gasmodel.com .

Keywords

Asymptotic normality
Consistency
Invertibility
Markov processes
Stationarity
Time-varying parameters

Access to Document

10.1016/j.jeconom.2021.06.003

Maximum likelihood estimation for score-driven modelsFinal published version, 785 KBLicence: Article 25fa Dutch Copyright Act

Persistent URL (handle)

Persistent link

Cite this

@article{f002f9e816704a24b05944dda23f9aff,

title = "Maximum likelihood estimation for score-driven models",

abstract = "We establish strong consistency and asymptotic normality of the maximum likelihood estimator for stochastic time-varying parameter models driven by the score of the predictive conditional likelihood function. For this purpose, we formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality both under correct specification and misspecification of the model. A detailed illustration is provided for a conditional volatility model with disturbances from the Student's t distribution.",

keywords = "Asymptotic normality, Consistency, Invertibility, Markov processes, Stationarity, Time-varying parameters",

author = "Francisco Blasques and {van Brummelen}, Janneke and Koopman, {Siem Jan} and Andr{\'e} Lucas",

note = "Funding Information: We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Amsterdam; the ?7th International Conference on Computational and Financial Econometrics?, London; the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation, (DNRF78). An overview of contributions on score-driven models is provided at http://gasmodel.com. Funding Information: We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Amsterdam; the ”7th International Conference on Computational and Financial Econometrics”, London; the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005 ) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099 ) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation , ( DNRF78 ). An overview of contributions on score-driven models is provided at http://gasmodel.com . Publisher Copyright: {\textcopyright} 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",

year = "2022",

month = apr,

doi = "10.1016/j.jeconom.2021.06.003",

language = "English",

volume = "227",

pages = "325--346",

journal = "Journal of Econometrics",

issn = "0304-4076",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Maximum likelihood estimation for score-driven models

AU - Blasques, Francisco

AU - van Brummelen, Janneke

AU - Koopman, Siem Jan

AU - Lucas, André

N1 - Funding Information: We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Amsterdam; the ?7th International Conference on Computational and Financial Econometrics?, London; the ?Workshop on Dynamic Models driven by the Score of Predictive Likelihoods?, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation, (DNRF78). An overview of contributions on score-driven models is provided at http://gasmodel.com. Funding Information: We thank Peter Boswijk, Christian Francq, Andrew Harvey, Anders Rahbek, the editor, associate editor, and two anonymous referees, as well as participants of the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Amsterdam; the ”7th International Conference on Computational and Financial Econometrics”, London; the ”Workshop on Dynamic Models driven by the Score of Predictive Likelihoods”, Tenerife; the IAAE London conference; and seminar participants at Vrije Universiteit Amsterdam, University of Cologne, CREST Paris, Maastricht University, for helpful comments and discussions. Blasques and Lucas thank the Dutch Research Council (NWO; grant VICI453-09-005 ) for financial support. Blasques thanks the Dutch Research Council (NWO; grant VI.Vidi.195.099 ) for financial support. Koopman acknowledges support from CREATES, Aarhus University, Denmark, funded by the Danish National Research Foundation , ( DNRF78 ). An overview of contributions on score-driven models is provided at http://gasmodel.com . Publisher Copyright: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2022/4

Y1 - 2022/4

N2 - We establish strong consistency and asymptotic normality of the maximum likelihood estimator for stochastic time-varying parameter models driven by the score of the predictive conditional likelihood function. For this purpose, we formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality both under correct specification and misspecification of the model. A detailed illustration is provided for a conditional volatility model with disturbances from the Student's t distribution.

AB - We establish strong consistency and asymptotic normality of the maximum likelihood estimator for stochastic time-varying parameter models driven by the score of the predictive conditional likelihood function. For this purpose, we formulate primitive conditions for global identification, invertibility, strong consistency, and asymptotic normality both under correct specification and misspecification of the model. A detailed illustration is provided for a conditional volatility model with disturbances from the Student's t distribution.

KW - Asymptotic normality

KW - Consistency

KW - Invertibility

KW - Markov processes

KW - Stationarity

KW - Time-varying parameters

UR - http://www.scopus.com/inward/record.url?scp=85110630967&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85110630967&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2021.06.003

DO - 10.1016/j.jeconom.2021.06.003

M3 - Article

AN - SCOPUS:85110630967

SN - 0304-4076

VL - 227

SP - 325

EP - 346

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -

Maximum likelihood estimation for score-driven models

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Persistent URL (handle)

Other files and links

Fingerprint

Cite this