Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T08:04:10.229Z Has data issue: false hasContentIssue false
  • English
  • Français

A new autoregressive time series model in exponential variables (NEAR(1))

Published online by Cambridge University Press:  01 July 2016

A. J. Lawrance  and
P. A. W. Lewis
A. J. Lawrance*
Affiliation:
University of Birmingham
P. A. W. Lewis*
Affiliation:
Naval Postgraduate School, Monterey
*
∗Postal address: Department of Statistics, The University of Birmingham, P.O. Box 363, Birmingham B15 2TT, U.K.
∗∗Postal address: Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

A new time series model for exponential variables having first-order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (ear(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of directional effects in sample path behaviour. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and autocorrelations are investigated. A transformed version of the model has a uniform marginal distribution and its correlation and regression structures are also obtained. Estimation aspects of the models are briefly considered.

Keywords

AUTOREGRESSIVE MODEL IN EXPONENTIAL VARIABLESNEGATIVE CORRELATIONCROSS-COUPLED PROCESSESANTITHETIC VARIABLESCORRELATED UNIFORM PROCESSTIME SERIESPOINT PROCESSSIMULATION
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 4 , December 1981 , pp. 826 - 845
Copyright
Copyright © Applied Probability Trust 1981 

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.)

Footnotes

Research supported by the U.K. Science and Engineering Research Council (Grant A185193), the U.S. Office of Naval Research (Grant NR-42-284) and the Naval Postgraduate School Foundation.

References

Gaver, D. P. (1972) Point process problems in reliability. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 775–800.Google Scholar
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
Jacobs, P. A. and Lewis, P. A. W. (1977) A mixed autoregressive-moving average exponential sequence and point process, earma(1, 1). Adv. Appl. Prob. 9, 87–104.CrossRefGoogle Scholar
Lawrance, A. J. (1980) Some autoregressive models for point processes. Point Processes and Queueing Problems (Colloquia Mathematica Societatis János Bólyai 24), ed. Bartfai, P. and Tomko, J., North Holland, Amsterdam, 257–275.Google Scholar
Lawrance, A. J. and Lewis, P. A. W. (1979) Simulation of some autoregressive Markovian sequences of positive random variables. In Proc. 1979 Winter Simulation Conference, ed. Highland, H. J., Spiegel, M. G., Shannon, R. J., IEEE, New York, 301–307.Google Scholar
Lawrance, A. J. and Lewis, P. A. W. (1980) The exponential autoregressive-moving average earma(p, q) process. J. R. Statist. Soc. B 42, 150–161.Google Scholar
Moran, P. A. P. (1967) Testing for correlation between non-negative variables. Biometrika 54, 385–394.Google Scholar
Raftery, A. E. (1980a) Un processus autoregressif à loi martingale exponentielle: propriétés asymptotiques et estimation de maximum de vraisemblance. Annales Scientifiques de l'Université de Clermont. Google Scholar
Raftery, A. E. (1980b) Estimation efficace pour un processus autoregressif exponentiel à densité discontinue. Publ. Inst. Statist. Univ. Paris 25, 64–90.Google Scholar
Vervaat, W. (1979) On a stochastic difference equation and a representation of non-negative infinitely divisible random variables. Adv. Appl. Prob. 11, 750–783.Google Scholar