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Hybrid simulation scheme for volatility modulated moving average fields

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We develop a simulation scheme for a class of spatial stochastic processes called volatility modulated moving averages. A characteristic feature of this model is that the behaviour of the moving average kernel at zero governs the roughness of realisations, whereas its behaviour away from zero determines the global properties of the process, such as long range dependence. Our simulation scheme takes this into account and approximates the moving average kernel by a power function around zero and by a step function elsewhere. For this type of approach, Bennedsen et al. (2017), who considered an analogous model in one dimension, coined the term hybrid simulation scheme. We derive the asymptotic mean square error of the simulation scheme and compare it in a simulation study with several other simulation techniques and exemplify its favourable performance in a simulation study.

Original languageEnglish
Pages (from-to)224-244
Number of pages21
Publication statusPublished - Dec 2019

    Research areas

  • ESTIMATORS, FRACTAL DIMENSION, MODELS, Matern covariance, Moving average, REPRESENTATIONS, Random field, SERIES, STOCHASTIC VOLATILITY, Stochastic volatility, simulation

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