BetaBit: A fast generator of autocorrelated binary processes for geophysical research

¹ School of Civil Engineering and Geosciences, Newcastle University - Newcastle Upon Tyne, NE1 7RU, UK
² Willis Research Network - 51 Lime St., London, EC3M 7DQ, UK
³ Dipartimento di Ingegneria, Università degli Studi Roma Tre - Via Vito Volterra 62, 00146 Rome, Italy

^(a) francesco.serinaldi@ncl.ac.uk

Received: 4 February 2017
Accepted: 21 June 2017

Abstract

We introduce a fast and efficient non-iterative algorithm, called BetaBit, to simulate autocorrelated binary processes describing the occurrence of natural hazards, system failures, and other physical and geophysical phenomena characterized by persistence, temporal clustering, and low rate of occurrence. BetaBit overcomes the simulation constraints posed by the discrete nature of the marginal distributions of binary processes by using the link existing between the correlation coefficients of this process and those of the standard Gaussian processes. The performance of BetaBit is tested on binary signals with power-law and exponentially decaying autocorrelation functions (ACFs) corresponding to Hurst-Kolmogorov and Markov processes, respectively. An application to real-world sequences describing rainfall intermittency and the occurrence of strong positive phases of the North Atlantic Oscillation (NAO) index shows that BetaBit can also simulate surrogate data preserving the empirical ACF as well as signals with autoregressive moving average (ARMA) dependence structures. Extensions to cyclo-stationary processes accounting for seasonal fluctuations are also discussed.