Gamma Processes

Abstract

The Beta Gamma transformation is described and is used to define a very simple first order autoregressive Beta Gamma process, BGAR(1). Maximum likelihood estimation is discussed for this model, as well as moment estimators. The first-order structure is extended to include moving average processes and mixed first-order autoregressive, pth-order moving average processes. It is shown that these Gamma processes are time-reversible and, therefore, too narrow for general physical modelling. A dual process to the BGAR(1) process, DBGAR(1), is introduced, as well as an iterated process which combines the Beta-Gamma process and the GAR(1) process of Gaver and Lewis (1980). Some properties of these extended autoregressive processes are derived. Several highly nonlinear extensions of these processes which produce negative correlation are given. Keywords: Beta Gamma Transformation; Beta Gamma Process, Moving Average Processes; Autoregressive Process; Gamma Innovation.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1986
Accession Number
ADA165390

Entities

People

  • D. K. Hugus
  • E. Mckenzie
  • Peter A. W. Lewis

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Computers
  • Data Science
  • Estimators
  • Gaussian Processes
  • Information Science
  • Maximum Likelihood Estimation
  • Military Research
  • Probability
  • Random Variables
  • Reversible
  • Schools
  • Sequences
  • Stationary Processes
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics

Fields of Study

  • Mathematics

Readers

  • Nuclear and Radiation Engineering.
  • Statistical inference.