Journal
JOURNAL OF BUSINESS & ECONOMIC STATISTICS
Volume 40, Issue 3, Pages 980-994Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/07350015.2021.1889568
Keywords
Martingale difference divergence matrix; Martingale difference hypothesis; Multivariate time series models; Specification test; Wild bootstrap
Funding
- National Social Science Fund of China [20BTJ041]
- Guangdong Basic and Applied Basic Research Foundation [2020A1515010821]
- Fundamental Research Funds for the Central Universities [12619624, 19JNYH08]
- GRF, RGC of Hong Kong [17306818, 17305619]
- NSFC [11690014, 11731015]
- Seed Fund for Basic Research [201811159049]
- NSF-DMS [1807023, 2014018]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [2014018] Funding Source: National Science Foundation
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1807023] Funding Source: National Science Foundation
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This article introduces a new class of tests to examine whether the error term is a martingale difference sequence in a multivariate time series model with parametric conditional mean, based on the martingale difference divergence matrix (MDDM). The tests are consistent for detecting fixed alternatives and have nontrivial power against local alternatives. Additionally, a wild bootstrap procedure is proposed to approximate critical values for the tests, which is theoretically valid.
This article proposes a general class of tests to examine whether the error term is a martingale difference sequence in a multivariate time series model with parametric conditional mean. These new tests are formed based on recently developed martingale difference divergence matrix (MDDM), and they provide formal tools to test the multivariate martingale difference hypothesis in the literature for the first time. Under suitable conditions, the asymptotic null distributions of these MDDM-based tests are established. Moreover, these MDDM-based tests are consistent to detect a broad class of fixed alternatives, and have nontrivial power against local alternatives of order n(-1/2), where n is the sample size. Since the asymptotic null distributions depend on the data generating process and the parameter estimation, a wild bootstrap procedure is further proposed to approximate the critical values of these MDDM-based tests, and its theoretical validity is justified. Finally, the usefulness of theseMDDM-based tests is illustrated by simulation studies and one real data example.
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