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1 results

  • An exponential moving-average sequence and point process (EMA1)

  • A. J. Lawrance, P. A. W. Lewis
  • Journal:
    Journal of Applied Probability / Volume 14 / Issue 1 / March 1977
    Published online by Cambridge University Press:
    14 July 2016, pp. 98-113
    Print publication:
    March 1977

  • A construction is given for a stationary sequence of random variables {Xi} which have exponential marginal distributions and are random linear combinations of order one of an i.i.d. exponential sequence {εi}. The joint and trivariate exponential distributions of Xi−1, Xi and Xi+ 1 are studied, as well as the intensity function, point spectrum and variance time curve for the point process which has the {Xi} sequence for successive times between events. Initial conditions to make the point process count stationary are given, and extensions to higher-order moving averages and Gamma point processes are discussed.