In this article, we introduce autoregressive processes with Esscher transformed Laplace distribution as stationary marginal distribution. Esscher transformed Laplace distribution is a subclass of one parameter exponential family and an alternative to various types of asymmetric Laplace distributions. The innovation structure of the process is derived and the parameters are estimated. Various properties of the processes are discussed and sample path behavior, forward and backward regressions, distribution of sums and joint distribution of contiguous observations of the process are studied. A new distribution called geometric Esscher transformed Laplace distribution is also introduced and the corresponding autoregressive processes are addressed. The relevance of the model and processes is established using real data. Various applications of the model are discussed.

autoregressive processes, Esscher transformation, Esscher transformed Laplace distribution, geometric Esscher transformed Laplace distribution, time series modeling.