Skip to main content Accessibility help

A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)

  • P. A. Jacobs (a1) and P. A. W. Lewis (a2)


A stationary sequence of random variables with exponential marginal distributions and the correlation structure of an ARMA (1, 1) process is defined. The process is formed as a random linear combination of i.i.d. exponential random variables and is very simple to generate on a computer. Moments and joint distributions for the sequence are obtained, as well as limiting properties of sums of the random variables and of the point process whose intervals have the EARMA (1, 1) structure.



Hide All
Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.
Box, G. E. P. and Jenkins, G. M. (1970) Time Series Analysis Forecasting and Control. Holden-Day, San Francisco.
Çinlar, E. (1969) On semi-Markov processes on arbitrary spaces. Proc. Camb. Phil. Soc. B 66, 381392.
Çinlar, E. (1975) Introduction to Stochastic Processes. Prentice-Hall, New Jersey.
Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London; Wiley, New York.
Doob, J. L. (1953) Stochastic Processes. Wiley, New York.
Gaver, D. P. and Lewis, P. A. W. (1977) First order autoregressive Gamma sequences and point processes. To appear.
Jacod, J. (1971) Théorème de renouvellement et classification pour les chaînes semi-markoviennes. Ann. Inst. H. Poincaré, 7 (2), 83129.
Lawrance, A. J. and Lewis, P. A. W. (1977) A moving average exponential point process (EMA1). J. Appl. Prob. 14, 98113.
Lewis, P. A. W. (1977) Generation of Gamma and mixed exponential time series with controlled dependence. To appear.
Rosenblatt, M. (1971) Markov Processes. Structure and Asymptotic Behaviour. Springer-Verlag, Berlin.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed