Continuous-time autoregressive models excited by semi-Lévy process for cyclostationary signal analysis

Abstract

In non-stationary signal modeling, it is critical to find an appropriate theoretical model with proper properties for analysing data. Models with cyclostationary (CS) property are prominent in signal processing analysis. In this paper, we extend the stationary Lévy driven continuous-time autoregressive (CAR) model to the semi-Lévy driven CAR (SL-CAR) model, which we show that has CS property. This model provides a platform for modeling non-stationary continuous-time processes. Using sample spectral coherence test, the CS behavior of simulated data from the SL-CAR(2) model is shown. Estimation of the parameters is followed by fitting VAR-GARCH process to the discretized state process and minimizing the distance between the covariance matrices of corresponding noise vectors. Numerical simulations provide evidence that the estimators are consistent, which is followed by computing the mean square errors. By using equally spaced sampling, the modes of empirical probability density functions of the estimators converge to the true values of the parameters when the sample size increases. Finally, we apply the SL-CAR(2) for modeling electrocardiogram biomedical signals and evaluate its performance.