Tests for Autocorrelation and Randomness in Multiple Time Series
多元时间序列的自相关与随机性检验AI 解读 ↓
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多元时间序列的自相关与随机性检验
- 研究问题
- 多元时间序列自相关和随机性检验的渐近分布在小样本中近似不足时，如何修改统计量以改善有限样本校准？
- 方法与思路
- 作者以高斯假设下推导的精确均值与协方差替代标准化中的渐近矩，并用样本估计替代干扰参数，开展模拟检验。
- 材料陈述的贡献
- 摘要称，修改统计量与原统计量渐近等价，却在较小样本中获得更好的分布近似；非正态情形也可能受益。
- 阅读关注点
- 应核对精确矩推导的高斯条件、干扰参数代入影响，以及模拟中的样本规模、维度、非正态设定和近似评价标准。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明。精确矩依赖高斯假设；非正态改善仅为摘要所述可能性，未给出普遍保证或模拟数值。
原文摘要
There exist several tests for autocorrelation and randomness in multiple time series. Unfortunately, the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples. In this article, the test statistics are modified. Asymptotically, these modified statistics are equivalent to their original counterparts; however, it is found that the asymptotic distributions of these statistics provide adequate approximation to the exact ones in relatively small samples and possibly when the time series are nonnormal. The adequacy of the approximations is examined by simulation experiments. The original test statistics are based on sample lag cross-covariances, autocovariances, cross-correlations, and autocorrelations standardized by their asymptotic means and covariances. The modified statistics are obtained when the asymptotic means and covariances in the standardization are replaced by the exact means and covariances. The expressions for these moments are derived on the assumption that the time series is Gaussian. These moments (both asymptotic and exact) involve nuisance parameters. In constructing the test statistics, these nuisance parameters are replaced by their sample counterparts, which are consistent estimates of the parameters.