Jinyuan Chang, Qing Jiang, Xiaofeng Shao
arXiv 11 Sep 2022 · Econometrics · publishedJournal of Econometrics (2022) · 16 citations (OpenAlex)
arXiv:2209.04770 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at different lags. To conduct the inference, we approximate the null distribution of our test statistic by Gaussian approximation and provide a simulation-based approach to generate critical values. The asymptotic behavior of the test statistic under the alternative is also studied. Our approach is nonparametric as the null hypothesis only assumes the time series concerned is martingale difference without specifying any parametric forms of its conditional moments. As an advantage of Gaussian approximation, our test is robust to the cross-series dependence of unknown magnitude. To the best of our knowledge, this is the first valid test for the martingale difference hypothesis that not only allows for large dimension but also captures nonlinear serial dependence. The practical usefulness of our test is illustrated via simulation and a real data analysis. The test is implemented in a user-friendly R-function.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Chang, Chen and Wu (2021) Central limit theorems for high dimensional dependent data | 1.000 | 8 | 5 | 100% |
| 2 | Chang, Yao and Zhou (2017) Testing for high-dimensional white noise using maximum cross correlations | 1.000 | 8 | 3 | 100% |
| 3 | Chernozhukov et al (2019) Inference on causal and structural parameters using many moment inequalities | 1.000 | 7 | 3 | 100% |
| 4 | Andrews (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation | 1.000 | 5 | 3 | 100% |
| 5 | Hong, Linton and Zhang (2017) An investigation into multivariate variance ratio statistics and their application to stock market predictability | 0.954 | 23 | 6 | 87% |
| 6 | Zhang and Cheng (2018) Gaussian approximation for high dimensional vector under physical dependence | 0.874 | 5 | 2 | 100% |
| 7 | Zhang and Wu (2017) Gaussian approximation for high dimensional time series | 0.874 | 5 | 2 | 100% |
| 8 | Chernozhukov, Chetverikov and Kato (2017) Central limit theorems and bootstrap in high dimensions | 0.794 | 6 | 4 | 50% |
| 9 | Chang, Tang and Wu (2013) Marginal empirical likelihood and sure independence feature screening | 0.737 | 3 | 3 | 67% |
| 10 | Escanciano and Velasco (2006) Generalized spectral tests for the martingale difference hypothesis | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 70 scored citations.