Test Consistency with Varying Sampling Frequency
采样频率变化下的检验一致性AI 解读 ↓
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采样频率变化下的检验一致性
- 研究问题
- 当样本量增加且等距采样间隔随之改变时，观测跨度和采样频率如何影响单位根检验与随机性检验的一致性及功效？
- 方法与思路
- 作者允许采样间隔沿不同路径变化，分析基于原序列或一阶差分的一阶相关系数检验，并用蒙特卡洛考察有限样本功效。
- 材料陈述的贡献
- 摘要称不同检验需要不同的跨度增长条件；差分序列上的单位根检验针对平稳备择要求跨度增长快于样本量平方根。
- 阅读关注点
- 应核对各检验的原假设、备择与统计量，以及跨度、间隔和样本量的关系；同时核对模拟设计和采样频率的用语。
- 阅读边界
- 仅据所给 Crossref 摘要；完整条件与模拟数值未提供，结论针对所研究的相关系数检验，不能推广到所有单位根检验。
原文摘要
This paper considers the consistency property of some test statistics based on a time series of data. While the usual consistency criterion is based on keeping the sampling interval fixed, we let the sampling interval take any equispaced path as the sample size increases to infinity. We consider tests of the null hypotheses of the random walk and randomness against positive autocorrelation (stationary or explosive). We show that tests of the unit root hypothesis based on the first-order correlation coefficient of the original data are consistent as long as the span of the data is increasing. Tests of the same hypothesis based on the first-order correlation coefficient of the first-differenced data are consistent against stationary alternatives only if the span is increasing at a rate greater than T ½ , where T is the sample size. On the other hand, tests of the randomness hypothesis based on the first-order correlation coefficient applied to the original data are consistent as long as the span is not increasing too fast. We provide Monte Carlo evidence on the power, in finite samples, of the tests Studied allowing various combinations of span and sampling frequencies. It is found that the consistency properties summarize well the behavior of the power in finite samples. The power of tests for a unit root is more influenced by the span than the number of observations while tests of randomness are more powerful when a small sampling frequency is available.