Statistical comparison of time series is useful for the detection of mechanical damage and many other real-world applications. New methods have been proposed to check whether two semi-stationary time series have the same normalized dynamics. The proposed methods differ from traditional methods in that they are based on the Laplace periodogram, which is a robust tool to analyze the serial dependence of time series. Via the method of estimating equations, a generalized score statistic and an order selected statistic are developed for the comparison. Their asymptotic distributions under the null are obtained. The proposed methods are applicable to compare two semi-stationary time series which may be dependent on each other. They also can be used to compare two time series whose traditional spectral densities or autocovariance structures may not exist. A Monte Carlo simulation study illustrates the validity of the asymptotic results and the finite sample performance. The proposed methods have been applied to an analysis of non-stationary vibration signals for mechanical damage detection.

时间序列的统计比较对于检测机械损伤和许多其他实际应用非常有用。已经提出了新的方法来检查两个半平稳时间序列是否具有相同的归一化动力学。所提出的方法与传统方法的不同之处在于它们基于拉普拉斯周期图，这是分析时间序列的序列依赖性的强大工具。通过估计方程的方法，开发了广义得分统计量和顺序选择统计量以进行比较。得到了它们在零下的渐近分布。所提出的方法适用于比较两个相互依赖的半平稳时间序列。它们还可以用于比较两个时间序列，而这两个时间序列可能不存在传统的频谱密度或自协方差结构。蒙特卡洛模拟研究证明了渐近结果的有效性和有限的样本性能。所提出的方法已应用于非平稳振动信号的分析，以进行机械损伤检测。