Abstract

Checking whether the error term is a marginal difference sequence

(MDS) in the multivariate time series model with a parametric conditional

mean is a crucial problem. Tests based on the martingale difference divergence matrix (MDDM) are an effective statistical method for testing MDS

in the residuals of multivariate time series models. However, MDDM-based

tests require specifying the lag order. To solve this problem, we propose a

data-driven MDDM-based test that automatically selects the lag order. This

method has three main advantages: first, researchers do not need to specify

the lag order while the test automatically selects it from the data; second,

under the null hypothesis, the lag order is one; third, the proposed automatic

tests have good performance in detecting model inadequacy caused by highorder dependence. In theory, we prove the asymptotical property of the pro-

posed method. Furthermore, we demonstrate the effectiveness of this method

through simulations and real data analysis.

Information

Preprint No.SS-2024-0035
Manuscript IDSS-2024-0035
Complete AuthorsChenglong Zhong, Guochang Wang
Corresponding AuthorsGuochang Wang
Emailswanggc023@amss.ac.cn

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Acknowledgments

The authors greatly appreciate the very helpful comments and suggestions of two anonymous referees, associate editor, and co-editor. This work is partially supported by the

National Science Foundation of China (No.12271213), Guangdong Basic and Applied Basic Research Foundation (No.32224156).

Supplementary Materials

The oline Supplementary Material contains some additional simulation results as well as

the proofs of all theorems and lemmas in the paper.

Supplementary materials are available for download.