Abstract
Slepian models are derived for a stochastic process observed at level crossings of a moving average driven by a gaussian or Laplace noise. In particular, a Slepian model for the noise – the Slepian noise – is developed. For Laplace moving average process a method of sampling from the Slepian noise is also obtained by a Gibbs sampler. This facilitates comparison of behavior at crossing of a level between a gaussian process and a non-gaussian one and allows to study a random processes sampled at crossings of a non-gaussian moving average process. In a numerical study based on the method it is observed that the behavior of a non-gaussian moving average process at high level crossings is fundamentally different from that for the gaussian case, which is in line with some recent theoretical results on the subject.
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Podgórski, K., Rychlik, I. & Wallin, J. Slepian noise approach for gaussian and Laplace moving average processes. Extremes 18, 665–695 (2015). https://doi.org/10.1007/s10687-015-0227-z
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DOI: https://doi.org/10.1007/s10687-015-0227-z
Keywords
- Rice formula
- Level crossings
- Generalized Laplace distribution
- Moving average process
- Extreme episodes
- Tilted Rayleigh distribution
- Generalized inverse gaussian distribution