FIRST-ORDER INTEGER-VALUED AUTOREGRESSIVE (INAR(1)) PROCESS

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Discrete Analogues of Self-Decomposability and Stability

F. Steutel, K. van Harn (1979)

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On Conditional Least Squares Estimation for Stochastic Processes

Paul Nelson, Lawrence A. Klimko (1978)

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First-order autoregressive gamma sequences and point processes

D P Gaver, P. A. W Lewis (1980)

It is shown that there is an innovation process {∊ n } such that the sequence of random variables { X n } generated by the linear, additive first-order autoregressive scheme X n = p X n-1 + ∊ n are marginally distributed as gamma (λ, k ) variables if 0 ≦ p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

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Journal

Title: Journal of Time Series Analysis

Abbreviated Title: J Time Series Analysis

Publisher: Wiley-Blackwell

ISSN (Print): 0143-9782

ISSN (Electronic): 1467-9892

Publication date Created: May 1987

Publication date (Print): May 1987

Volume: 8

Issue: 3

Pages: 261-275

Article

DOI: 10.1111/j.1467-9892.1987.tb00438.x

SO-VID: 16e95f66-1af3-44c0-98d0-5e7a6873b3cf

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http://doi.wiley.com/10.1002/tdm_license_1.1

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FIRST-ORDER INTEGER-VALUED AUTOREGRESSIVE (INAR(1)) PROCESS

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Abstract

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Procedural speed in criminal law

Most cited references 6

Discrete Analogues of Self-Decomposability and Stability

On Conditional Least Squares Estimation for Stochastic Processes

First-order autoregressive gamma sequences and point processes

Author and article information

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