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ASYMPTOTICS FOR TIME-VARYING VECTOR MA($\infty $) PROCESSES

Published online by Cambridge University Press:  09 January 2024

Yayi Yan ,
Jiti Gao Open the ORCID record for Jiti Gao [Opens in a new window]  and
Bin Peng Open the ORCID record for Bin Peng [Opens in a new window]
Yayi Yan
Affiliation:
Shanghai University of Finance and Economics and Monash University
Jiti Gao*
Affiliation:
Monash University
Bin Peng
Affiliation:
Monash University
*
Address correspondence to Jiti Gao, Department of Econometrics and Business Statistics, Monash University, Caulfield East, VIC 3145, Australia; e-mail: Jiti.Gao@monash.edu.
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Abstract

This paper introduces a new class of time-varying vector moving average processes of infinite order. These processes serve dual purposes: (1) they can be used to model time-varying dependence structures, and (2) they can be used to establish asymptotic theories for multivariate time series models. To illustrate these two points, we first establish some fundamental asymptotic properties and use them to infer the trending term of a vector moving average infinity process. We then investigate a class of time-varying VARX models. Finally, we demonstrate the empirical relevance of the theoretical results using extensive simulated and real data studies.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 33
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Footnotes

The authors of this paper would like to thank the Co-Editor, Yixiao Sun, and two referees for their constructive comments. Thanks also go to George Athanasopoulos, Rainer Dahlhaus, David Frazier, Oliver Linton, Gael Martin, Peter C. B. Phillips, and Wei Biao Wu for their helpful comments on earlier versions of this paper. Yan acknowledges the financial support of the National Natural Science Foundation of China (Grant No. 72303142) and Fundamental Research Funds for the Central Universities (Grant Nos. 2022110877 & 2023110099). Both Gao and Peng acknowledge the Australian Research Council Discovery Grants Program for its financial support under Grant Numbers: DP200102769 and DP210100476.

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