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1 results

  • Representations of continuous-time ARMA processes

  • Part of
  • Peter J. Brockwell
  • Journal:
    Journal of Applied Probability / Volume 41 / Issue A / 2004
    Published online by Cambridge University Press:
    14 July 2016, pp. 375-382
    Print publication:
    2004

  • Using the kernel representation of a continuous-time Lévy-driven ARMA (autoregressive moving average) process, we extend the class of nonnegative Lévy-driven Ornstein–Uhlenbeck processes employed by Barndorff-Nielsen and Shephard (2001) to allow for nonmonotone autocovariance functions. We also consider a class of fractionally integrated Lévy-driven continuous-time ARMA processes obtained by a simple modification of the kernel of the continuous-time ARMA process. Asymptotic properties of the kernel and of the autocovariance function are derived.