Abstract
This paper introduces the class of quasi score-driven (QSD) models. This new class inherits and extends the basic ideas behind the development of score-driven (SD) models and addresses a number of unsolved issues in the score literature. In particular, the new class of models (i) generalizes many existing models, including SD models, (ii) disconnects the updating equation from the log-likelihood implied by the conditional density of the observations, (iii) allows testing of the assumptions behind SD models that link the updating equation of the conditional moment to the conditional density, (iv) allows QML estimation of SD models, (v) and allows explanatory variables to enter the updating equation. We establish the asymptotic properties of the QLE, QMLE and MLE of the proposed QSD model as well as the likelihood ratio and Lagrange multiplier test statistics. The finite sample properties are studied by means of an extensive Monte Carlo study. Finally, we show the empirical relevance of QSD models to estimate the conditional variance of 400 US stocks.
| Original language | English |
|---|---|
| Pages (from-to) | 251-275 |
| Number of pages | 25 |
| Journal | Journal of Econometrics |
| Volume | 234 |
| Issue number | 1 |
| Early online date | 25 Jan 2022 |
| DOIs | |
| Publication status | Published - May 2023 |
Bibliographical note
Funding Information:The authors gratefully acknowledge the editor Torben Andersen, the associate editor and two anonymous referees for insightful comments and suggestions, Kris Boudt, Paul Embrechts, Patrick Gagliardini, Peter Reinhard Hansen, Andrew Harvey, Elvezio Ronchetti, Bilel Sanhaji and Olivier Scaillet for helpful discussions as well as the participants of the GFRI seminar in Geneva, the Econometrics seminar at KULeuven, the Quantact seminar in Montreal, the Econometrics and Business Statistics seminar at CREATES in Aarhus and the 22nd Dynamic Econometrics Conference in Oxford. Francisco Blasques acknowledges the financial support of the Dutch Science Foundation (NWO) under grant Vidi.195.099 . Sébastien acknowledges research support by the French National Research Agency Grant ANR-17-EURE-0020 , and by the Excellence Initiative of Aix-Marseille University - A*MIDEX . Christian and Sébastien also acknowledge research support by the French National Research Agency Grant ANR-21-CE26-0007-01 . Christian also thanks the ECODEC labex .
Funding Information:
The authors gratefully acknowledge the editor Torben Andersen, the associate editor and two anonymous referees for insightful comments and suggestions, Kris Boudt, Paul Embrechts, Patrick Gagliardini, Peter Reinhard Hansen, Andrew Harvey, Elvezio Ronchetti, Bilel Sanhaji and Olivier Scaillet for helpful discussions as well as the participants of the GFRI seminar in Geneva, the Econometrics seminar at KULeuven, the Quantact seminar in Montreal, the Econometrics and Business Statistics seminar at CREATES in Aarhus and the 22nd Dynamic Econometrics Conference in Oxford. Francisco Blasques acknowledges the financial support of the Dutch Science Foundation (NWO) under grant Vidi.195.099. S?bastien acknowledges research support by the French National Research Agency Grant ANR-17-EURE-0020, and by the Excellence Initiative of Aix-Marseille University - A*MIDEX. Christian and S?bastien also acknowledge research support by the French National Research Agency Grant ANR-21-CE26-0007-01. Christian also thanks the ECODEC labex.
Publisher Copyright:
© 2022 Elsevier B.V.
Funding
The authors gratefully acknowledge the editor Torben Andersen, the associate editor and two anonymous referees for insightful comments and suggestions, Kris Boudt, Paul Embrechts, Patrick Gagliardini, Peter Reinhard Hansen, Andrew Harvey, Elvezio Ronchetti, Bilel Sanhaji and Olivier Scaillet for helpful discussions as well as the participants of the GFRI seminar in Geneva, the Econometrics seminar at KULeuven, the Quantact seminar in Montreal, the Econometrics and Business Statistics seminar at CREATES in Aarhus and the 22nd Dynamic Econometrics Conference in Oxford. Francisco Blasques acknowledges the financial support of the Dutch Science Foundation (NWO) under grant Vidi.195.099 . Sébastien acknowledges research support by the French National Research Agency Grant ANR-17-EURE-0020 , and by the Excellence Initiative of Aix-Marseille University - A*MIDEX . Christian and Sébastien also acknowledge research support by the French National Research Agency Grant ANR-21-CE26-0007-01 . Christian also thanks the ECODEC labex . The authors gratefully acknowledge the editor Torben Andersen, the associate editor and two anonymous referees for insightful comments and suggestions, Kris Boudt, Paul Embrechts, Patrick Gagliardini, Peter Reinhard Hansen, Andrew Harvey, Elvezio Ronchetti, Bilel Sanhaji and Olivier Scaillet for helpful discussions as well as the participants of the GFRI seminar in Geneva, the Econometrics seminar at KULeuven, the Quantact seminar in Montreal, the Econometrics and Business Statistics seminar at CREATES in Aarhus and the 22nd Dynamic Econometrics Conference in Oxford. Francisco Blasques acknowledges the financial support of the Dutch Science Foundation (NWO) under grant Vidi.195.099. Sébastien acknowledges research support by the French National Research Agency Grant ANR-17-EURE-0020, and by the Excellence Initiative of Aix-Marseille University - A*MIDEX. Christian and Sébastien also acknowledge research support by the French National Research Agency Grant ANR-21-CE26-0007-01. Christian also thanks the ECODEC labex.
Keywords
- Asymmetry
- Fat-tails
- GARCH
- QLE
- QMLE
- Score-driven models