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A Mixed Exponential Time Series Model

Author

Listed:
  • A. J. Lawrance

    (University of Birmingham, England)

  • P. A. W. Lewis

    (Naval Postgraduate School)

Abstract

The simple model NMEAR (1) is described for a stationary dependent sequence of random variables which have a mixed exponential marginal distribution; the model is a first-order stochastic difference equation with random coefficients and is first-order Markovian. It should be broadly applicable for stochastic modelling in operations analysis. In particular, it provides a model for simulating interarrival times in queuing systems when these random variables are overdispersed relative to an exponential random variable, and moreover are positively correlated. The model also has capability to model a variable which may be zero, but which otherwise is exponentially distributed. Such variables are found as waiting times in queuing models. Because of the (random) linearity of the process, it is easily extended to the modelling of cross-coupled sequences of interarrival and service times. The model can also be extended quite simply to a mixed exponential process with mixed pth order autoregressive and qth order moving average correlation structure, NMEAR (p, q), so that non-Markovian dependence can be handled.

Suggested Citation

  • A. J. Lawrance & P. A. W. Lewis, 1982. "A Mixed Exponential Time Series Model," Management Science, INFORMS, vol. 28(9), pages 1045-1053, September.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:9:p:1045-1053
    DOI: 10.1287/mnsc.28.9.1045
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    Cited by:

    1. Lekshmi, V. Seetha & Jose, K.K., 2006. "Autoregressive processes with Pakes and geometric Pakes generalized Linnik marginals," Statistics & Probability Letters, Elsevier, vol. 76(3), pages 318-326, February.
    2. Kozubowski, Tomasz J. & Podgórski, Krzysztof, 2010. "Random self-decomposability and autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1606-1611, November.

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