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Gamma processes

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Author
Lewis, Peter A. W.
Mckenzie, Edward
Hugus, David Kennedy
Date
1986-01
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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
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
URI
https://hdl.handle.net/10945/29889
NPS Report Number
NPS55-86-002
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