Published online by Cambridge University Press: 09 January 2024
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.
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.