Autoregressive processes with normal-Laplace marginals

The normal-Laplace distribution introduced by Reed and Jorgensen [Reed, W.J., Jorgensen, M., 2004. The double Pareto-lognormal distribution, A new parametric model for size distributions. Comm. Statist-Theory and Methods, 33, 1733-1753], is studied briefly. A first order autoregressive process with normal-Laplace stationary marginal distribution is introduced and various properties are discussed. The process gives a combination of Gaussian as well as non-Gaussian time series models for the first time and is free from the zero defect problem. Simulation studies are done and sample path properties are explored. Regression behaviour of the process is studied. The applications in modelling data from various contexts are also discussed.