A Statistical Time-Frequency Model for Non-stationary Time Series Analysis

Time-frequency analysis (TFA) plays an important role in various engineering and biomedical fields. For a non-stationary time series, a common practice is to divide data into segments under the piecewise stationarity assumption and perform TFA for each segment. In this article, we propose a three-layer latent variable model that relaxes such an assumption and therefore provides a more flexible solution to identify the frequency components and characterize their evolution over time for non-stationary time series with multi-component signals. Our proposed model is built upon hierarchical Dirichlet process (HDP), hidden Markov model (HMM) and extended time-varying autoregressive (ETVAR) model. The proposed approach does not impose any restrictions on the number and locations of segments, or the number and values of the frequency components within a segment. Both the simulation studies and real data applications demonstrate the superiority of the proposed method over existing methods.