Robust tests for time series comparison based on Laplace periodograms

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.