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首页> 外文会议>International Conference on Computational Science - ICCA 2003 Pt.1 Jun 2-4, 2003 Melbourne, Australia and St. Petersburg, Russia >Stochastic Simulation of Time Series by Using the Spatial-Temporal Weierstrass Function
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Stochastic Simulation of Time Series by Using the Spatial-Temporal Weierstrass Function

机译：使用时空Weierstrass函数的时间序列的随机模拟

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摘要

We extend the recently considered toy model of Weierstrass (or Levy) walks with varying velocity of the walker by introducing a more realistic possibility that the walk can be occasionally intermitted by its momentary localization; the localizations themselves are again described by the Weierstrass (or Levy) process. The direct empirical motivation for developing this combined model is, for example, the dynamics of financial high-frequency time series or meteorological ones. This approach makes it possible to study by efficient stochastic simulations the whole spatial-temporal range. To describe empirical data, which are collected at discrete time-steps, we used in the continuous-time series produced by the model a discretization procedure. We observed that such a procedure constitutes a basis for long-time autocorrelations (of the variation of the walker single-step displacements) which appear to be similar to those observed, e.g., in financial time series, although single steps of the walker within the continuous time are un-correlated.
机译：通过引入更现实的可能性，即步行有时会因其瞬时定位而中断，我们扩展了最近被认为是Weierstrass（或Levy）步行的玩具模型。本地化本身由Weierstrass（或Levy）过程再次描述。开发此组合模型的直接经验动机是，例如，金融高频时间序列的动态或气象动态。这种方法使通过有效的随机模拟研究整个时空范围成为可能。为了描述在离散时间步长收集的经验数据，我们在由模型产生的连续时间序列中使用了离散化程序。我们观察到，这样的程序构成了长时间自相关（助步器单步位移的变化）的基础，该自相关似乎类似于在金融时间序列中观察到的那些，尽管助步器在步长范围内是单步的。连续时间是不相关的。

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