Distance metrics for stationary time series based on cross-spectral methods and information theory
In this presentation, we introduced two distance rate measures for discrepancy growth between two stationary processes: the Jensen-distance rate (JDR) and variance-distance rate (VDR). Moreover, a Blackman-Tukey spectral density estimator was used to estimate the distance rates between two stationary processes. In particular, we examined the fractional noise as a specific case of a weakly stationary process. Numerical results demonstrate the estimation method's performance under Gaussian and non-Gaussian settings. The results highlight the good performance of the proposed estimators, where the estimated VDR closely match the theoretical ones when the fractional difference noise processes are stationary and Gaussian. For a non-Gaussian case, an application to an ozone monitoring network showcases the estimated JDR for time series data, highlighting the practical utility of the proposed distance rate in time series analysis.
Keywords: Jensen-variance distance; Stationary processes; Toeplitz matrices; Spectral density; Blackman–Tukey estimator; Information potential