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，如何调整统计量以改善其分布近似？
- 方法与思路
- 作者在高斯假设下推导相关样本矩的精确均值与协方差，用其替换标准化中的渐近矩，并以一致样本估计替代干扰参数。
- 材料陈述的贡献
- 摘要称，修正统计量与原统计量渐近等价，模拟支持其在较小样本中的分布近似改善，并提示可能适用于非正态序列。
- 阅读关注点
- 阅读全文时应核对各检验统计量的精确矩、干扰参数替代带来的影响，以及模拟如何评价小样本和非正态情形。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明，不能推断刊本变化；精确矩基于高斯假设，非正态适用性仅作可能性陈述。
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.