Time-Frequency Analysis for Non-Stationary Time Series Based on Adaptive Window

Time-frequency distribution is an important tool for analyzing time series, yet the application of traditional methods in non-stationary time series is constrained by their inherent limitations. This paper proposes a method that integrates the autoregressive model, the dynamic linear model, and adaptive windowing, enabling the dynamic partitioning of non-stationary time series into a series of locally stationary process. Within these segments, the relationship between the regression coefficients of the AR model and the frequency components is established. Simulation experiments demonstrate the effectiveness of our proposed approach in identifying locally stationary processes and extracting frequency components. Compared to the ShortTime Fourier Transform (STFT), our method can significantly enhance the concentration of the estimated time-frequency distribution. Furthermore, since the windows obtained by our method do not overlap in time, it avoids the aliasing phenomenon that often occurs in STFT due to windowing.