Phase-Rectified Signal Variance Series and its Values for a Stationary Gaussian Process

Phase-Rectified Signal Averaging (PRSA) computes the average of portions of a time series aligned at a given anchor point. In this study we explored the variance of such samples around the PRSA, or “Phase-Rectified Signal Variance” series (PRSV), and derived its analytical formulation for a stationary Gaussian process. The mathematical prediction was compared with estimates obtained from a set of synthetic time series generated using autoregressive models. The formula, which matched the numerical analysis, reveals interesting insights for the creation of new measures to quantify divergence from Gaussianity and stationarity, in addition to the well known acceleration and deceleration capacities.