A Test for a Class of Semi-Stationary Time Series with an Application to Vibration Data

Music City Center 

A time series is second-order stationary if both its mean and covariance structure remain constant over time. Many existing methods test for second-order stationarity, as it is a crucial assumption in the analysis of classical time series and certain stationary nonlinear time series. However, few methods are available to determine whether a time series is semi-stationary. If a time series is semi-stationary, it can be analyzed much more easily than a general non-stationary time series. In this paper, we propose a new time-domain test to assess whether the normalized frequency pattern of a non-stationary time series remains unchanged over time. A robust statistical method is developed, and its asymptotic distribution is derived. A simulation study is conducted to evaluate the finite-sample performance of the proposed method. Finally, we apply the proposed method to vibrational data to assess whether a mechanical system exhibits linear behavior within a certain range of inputs.

Dynamics

Periodogram

Spectral method

Robust

Semi-stationary

Vibration data 

Section on Physical and Engineering Sciences