Generalized normal-Laplace AR process

摘要

We introduce an autoregressive process called generalized normal-Laplace autoregressive process with generalized normal-Laplace distribution [Reed, W. J., 2007. Brownian-Laplace motion and its use in financial modelling. Comm. Statist. Theory Methods, 36,473-484], as stationary marginal distribution. Various properties of the distribution and the processes are discussed. The innovation structure is derived and estimation of parameters is addressed. Sample path behaviour, distribution of sums and the joint distribution of contiguous observations, etc. are studied. An algorithm for the generation of the process is also given as appendix.