Recurrence plots of discrete-time Gaussian stochastic processes

•We derive theoretical values of RP diagonal-based measures for Gaussian processes.•We illustrate our results on AR(1) processes and fractional Gaussian noise.•Our results provide a benchmark to improve estimation of the considered measures.

We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 11. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (RECREC) (ii) the percent determinism (DETDET) and (iii) RP-based estimation of the εε-entropy κ(ε)κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.