Detecting Periodic Components in a White Gaussian Time Series
提出一种基于最大周期图与截尾均值之比的统计量来检测白高斯序列中的周期成分，该检验在非零傅里叶频率下与Fisher检验渐近功效相同，但模拟显示对多峰备择假设更有效。
SUMMARY A family of tests for periodic components in a white Gaussian series is proposed. The test is based on a statistic which is proportional to the ratio of the maximum periodogram to a trimmed mean of the periodograms. The asymptotic distributions of the statistics are obtained. It is shown that the proposed test and Fisher's test have the same asymptotic powers against the alternative of a sinusoidal wave at a non-zero Fourier frequency. The simulation results suggest that the proposed test is more powerful than Fisher's test against the alternatives of multiple peaks. The problem of detecting multiple peaks is also discussed.