Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-17T14:59:32.808Z Has data issue: false hasContentIssue false
  • English
  • Français

A reversibility relationship for two Markovian time series models by stationary exponential tailed distribution

Part of: Inference from stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

R. P. Littlejohn
R. P. Littlejohn*
Affiliation:
AgResearch
*
∗ Postal address: AgResearch, Invermay Agricultural Centre, Private Bag, Mosgiel, New Zealand.
Get access Rights & Permissions [Opens in a new window]

Abstract

The continuous autoregressive and minification stationary non-negative time series models discussed by Chernick et al. (1988) are generalized to model marginal distributions which have atoms of mass at zero. The reversibility theorem relating these processes with exponential marginal distributions is extended to the case where the marginal distribution has exponential tail.

Keywords

EXPONENTIAL AUTOREGRESSIONMINIFICATION PROCESSNON-GAUSSIAN TIME SERIESMUTUALLY REVERSIBLE TIME SERIES

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Short Communications
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 575 - 581
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Chernick, M. R., Daley, D. J. and Littlejohn, R. P. (1988) A time-reversibility relationship between two Markov chains with stationary exponential distributions. J. Appl. Prob. 25, 418–422.Google Scholar
[2] Daley, D. J. (1992) Characterization of distributions with exponential and geometric tails. Ann. Prob. (Submitted) Google Scholar
[3] Gaver, D. P. and Lewis, P. A. W. (1980) First-order autoregressive gamma sequences and point processes. Adv. Appl. Prob. 12, 727–745.Google Scholar
[4] Hutton, J. L. (1990) Non-negative time series models for dry river flow. J. Appl. Prob. 27, 171–182.CrossRefGoogle Scholar
[5] Lawrance, A. J. and Lewis, P. A. W. (1981) A new autoregressive time series model in exponential variables (NEAR(1)). Adv. Appl. Prob. 13, 826–845.Google Scholar
[6] Lewis, P. A. W. and Mckenzie, E. (1991) Minification processes and their transformations. J. Appl. Prob. 28, 45–57.Google Scholar
[7] Littlejohn, R. P. (1992a) Discrete minification processes and reversibility. J. Appl. Prob. 29, 82–91.Google Scholar
[8] Littlejohn, R. P. (1992b) An operation which inverts Bernoulli multiplication and associated stationary reversible Markov processes. J. Appl. Prob. 29, 234–238.Google Scholar
[9] Littlejohn, R. P. (1993) A reversibility relationship for two Markovian time series with stationary geometric tailed distribution. In preparation.Google Scholar
[10] Raftery, A. E. (1982) Generalised non-normal time series models. In: Time Series Analysis: Theory and Practice 1 , ed. Anderson, O. D., pp. 621–640. North-Holland, Amsterdam.Google Scholar
[11] Tavares, L. V. (1980) An exponential Markovian stationary process. J. Appl. Prob. 17, 1117–1120. Addendum, J. Appl. Prob. 18, 957.Google Scholar