On Construction and Simulation of Autoregressive Sources With Near-Laplace Marginals

Abstract

In this paper, we focus upon the problem of modeling and simulation of stationary non-Gaussian time series. In particular, we consider a first order autoregressive process whose marginal distribution is close to the Laplace density. This model allows us to simulate correlated non-Gaussian signals typically appearing in speech analysis, compression, and noise synthesis. The Monte Carlo rejection method is applied to develop efficient algorithms for simulation of the proposed autoregressive process. We also extend our theory and algorithms to the related issue of constructing a correlated bivariate time-series model with near-Laplace margins. A theoretical analysis of the average complexity of the proposed simulation algorithms is included.