A Rank Based Method for Testing ARCH Effect and Serial Correlation of High-dimensional Time Series
This article proposes a hypothesis testing method to detect serial correla-tion and ARCH effect in high-dimensional time series based on L2 norm and Spearman's correlation.In this article,We study the asymptotic behavior of our test statistic and provide a bootstrap-based approach to generate critical values,we prove our test can control Type-Ⅰ errors.Our test is dimensional-free,which means it is independent of the dimension of the data,hence our test can be used for high dimensional time series data.Our test does not require tail properties of data,hence it can be used for heavy-tailed time series.The simulation results indicate that our new test performs well in both empirical sizes and powers and outperforms other tests.The practical usefulness of our test is illustrated via simulation and a real data analysis.
ARCH effecthigh-dimensional time seriesrank statisticsserial correlation
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