Local polynomial modelling of time-varying autoregressive processes and its application to the analysis of event-related electroencephalogram

This paper proposes a new method for identification of time-varying autoregressive (TVAR) models based on local polynomial modeling (LPM) and applies it to investigate the dynamic spectral information of event-related electroencephalogram (EEG). The proposed method models the TVAR coefficients locally by polynomials and estimates those using least-squares estimation with a kernel having a certain bandwidth. A data-driven variable bandwidth selection method is developed to obtain the optimal bandwidth, which minimizes the mean squared error (MSE). Simulation results show that the LPM-based TVAR identification method outperforms conventional methods for different scenarios. The advantages of the LPM method make it a useful high-resolution time-frequency analysis (TFA) technique for nonstationary biomedical signals like EEG. Experimental results show that the LPM method can reveal more meaningful time-frequency characteristics than wavelet transform.