题 目：Revised BDS Test

主讲人：罗文雅博士

时 间：2021年11月4日（周四）13：30-14：30

地 点：6号学院楼500会议室

主办单位：银河7163官网 浙江省2011“数据科学与大数据分析协同创新中心”

摘 要：

In this paper, we focus on the BDS test, which is a non-parametric test for independence. Its null hypothesis can be simply written as $H_{0}: \{u_{t}\}$ is i.i.d. (independent and identically distributed), where $\{u_{t}\}$ is a random sequence. Although the BDS test is widely used in economics and finance, it has a weakness that cannot be ignored: over-rejecting $H_{0}$ even if the length $T$ of $\{u_{t}\}$ is as large as $(100,1000)$. Since the correlation integral is the foundation of the BDS test, to improve the over-rejection problem, we accurately describe the expectation of the correlation integral, when $H_{0}$ is true. Besides, we calculate all terms of the asymptotic variance of the correlation integral whose order is $O(T^{-1})$ and $O(T^{-2})$, which is essential to improve the finite sample performance of the BDS test. Based on this, we further propose a revised BDS (RBDS) test and prove its asymptotic normality under $H_{0}$. The RBDS test not only inherits all the advantages of the BDS test, but also effectively corrects the over-rejection problem of the BDS test, which can be fully confirmed by the simulation results we presented in this paper. We also apply the RBDS test to some real data, aiming to illustrate that the performance of the RBDS test in practice is also encouraging.

主讲人简介：

罗文雅，理学博士。主要从事大维随机矩阵、时间序列、非参数统计等方面的研究。

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