Generalized Laplacian Distributions and Autoregressive Processes

Abstract

Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First- and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters. Various areas of application of these models are discussed.

Keywords:

• Autoregressive processes
• Bilateral gamma distribution
• Financial modeling
• Geometric generalized Laplacian distribution
• Geometric infinite divisibility
• Heavy-tailed distributions
• Hyperbolic distributions

Mathematics Subject Classification:

• Primary 60E05
• Secondary 62M10

Acknowledgment

The authors would like to thank the Department of Science and Technology, Government of India, New Delhi, for the financial assistance for this work under project number SR/S4/MS:287/05 and the Centre for Mathematical Sciences for providing all facilities. The authors are grateful to the Editor and the referee for the valuable suggestions and comments which helped in improving the article.