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TIME-VARYING PARAMETER REGRESSIONS WITH STATIONARY PERSISTENT DATA

Published online by Cambridge University Press:  01 April 2024

Zhishui Hu Open the ORCID record for Zhishui Hu [Opens in a new window] ,
Ioannis Kasparis Open the ORCID record for Ioannis Kasparis [Opens in a new window]  and
Qiying Wang Open the ORCID record for Qiying Wang [Opens in a new window]
Zhishui Hu
Affiliation:
University of Science and Technology of China
Ioannis Kasparis*
Affiliation:
University of Cyprus
Qiying Wang
Affiliation:
The University of Sydney
*
Address correspondence to Ioannis Kasparis, Department of Economics, University of Cyprus, Nicosia, Cyprus, email: kasparis@ucy.ac.cy.
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Abstract

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We consider local level and local linear estimators for estimation and inference in time-varying parameter (TVP) regressions with general stationary covariates. The latter estimator also yields estimates for parameter derivatives that are utilized for the development of time invariance tests for the regression coefficients. Our theoretical framework is general enough to allow for a wide range of stationary regressors, including stationary long memory. We demonstrate that neglecting time variation in the regression parameters has a range of adverse effects in inference, in particular, when regressors exhibit long-range dependence. For instance, parametric tests diverge under the null hypothesis when the memory order is strictly positive. The finite sample performance of the methods developed is investigated with the aid of a simulation experiment. The proposed methods are employed for exploring the predictability of SP500 returns by realized variance. We find evidence of time variability in the intercept as well as episodic predictability when realized variance is utilized as a predictor in TVP specifications.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 41 , Issue 4 , August 2025 , pp. 817 - 843
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

The authors thank the co-editor and two referees for their very helpful comments on the original version and revision of this paper. Hu acknowledges research support from the NSFC (Grant No. 11671373) and Wang acknowledges research support from the Australian Research Council.

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