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Keywords:

  • Non–negative time series;
  • ARMA processes;
  • extreme value estimator;
  • regular variation;
  • point processes
  • Primary: 62M10;
  • Secondary: 62E20;
  • 60F05

For moving average processes inline image where the coefficients are non-negative and the innovations are positive random variables with a regularly varying tail at infinity, we provide estimates for the coefficients based on the ratio of two sample values chosen with respect to an extreme value criteria. We then apply this result to obtain estimates for the parameters of non-negative ARMA models. Weak convergence results for the joint distribution of our estimates are established and a simulation study is provided to examine the small sample size behaviour of these estimates.