Abstract The BDS test is a test for detecting whether a random sequence is i.i.d. (independent and identically distributed). It has been used in economics and finance to examine whether a fitted time series model is adequate by examining whether the residual sequence is nearly i.i.d. Though the BDS test is widely used in the literature, it has a weakness of over-rejecting the null hypothesis even though the sample size T is as large as ( 100 , 1000 ) . In this study, we propose a modified BDS test (MBDS test) by removing some terms from the correlation integral, which is the foundation of the BDS test. Theoretical calculations and simulation results show that the MBDS test efficiently corrects the bias of the BDS test.

中文翻译：

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修改后的 BDS 测试

摘要 BDS检验是一种检测随机序列是否为iid（独立同分布）的检验。在经济学和金融学中，通过检验残差序列是否接近 iid 来检验拟合的时间序列模型是否充分虽然 BDS 检验在文献中被广泛使用，但它有一个弱点，即过度拒绝原假设，甚至尽管样本大小 T 与 (100, 1000) 一样大。在本研究中，我们通过从相关积分中删除一些项来提出一种改进的 BDS 测试（MBDS 测试），这是 BDS 测试的基础。理论计算和仿真结果表明，MBDS测试有效地纠正了BDS测试的偏差。