Methodologies Incorporating Cepstral Nulling for Time Series Cepstral Dissimilarity Evaluation

Abstract The most popular cepstral distances are computed as the square root of the weighted sum of squared differences of the cepstral coefficients. Traditionally, the coefficients are estimated from the time series measurements using autoregressive integrated moving average (ARIMA) models. The weights are also derived based on ARIMA models, and most of them are empirically set to zero. In this study, we adopt non-parametric methods to estimate the coefficients. Rather than setting the weights to zero, we set some of the estimated cepstral coefficients to zero independently for each time series. This procedure, known as cepstral nulling, has most commonly been applied in the context of periodogram smoothing. We explore five cepstral nulling approaches based on the Bayesian Information Criterion (BIC), Minimum Risk Inflation (MRI), Kolmogorov Structure Function (KSF), False Discovery Rate (FDR), and Familywise Error Rate (FER). As these techniques have not been previously applied to cepstral distance estimation, we evaluate their performance theoretically and empirically. To streamline the analysis, we prove only for BIC and MRI asymptotic results that elucidate their performance. The performance of all five cepstral nulling methods is demonstrated in experiments with simulated data. Furthermore, we also assess the effect of the use of cepstral nulling in the evaluation of the cepstral distances employed in clustering of the simulated data. In experiments with real-life data (ECG signals), we show that the best clustering result is achieved when the cepstral coefficients are thresholded using the MRI method.