MARKOV PROPERTIES OF HIGH FREQUENCY EXCHANGE RATE DATA
MARKOV PROPERTIES OF HIGH FREQUENCY EXCHANGE RATE DATA
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高频汇率数据的马尔可夫特性
DOI：
10.1016/s0378-4371(01)00269-2
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发表时间：
2000
影响因子：
0.5
通讯作者：
U. Stuttgart
中科院分区：
文献类型：
--
作者：
C. Renner;J. Peinke;R. F. U. O. Oldenburg;U. Stuttgart
我们提出了一个随机分析的数据集，包括106报价的美元对德国马克汇率。证明了在不同延迟时间τ上的价格变化x（τ）可以描述为在τ上演化的马尔可夫过程。因此，概率密度函数（pdf）p（x，τ）对延迟时间τ的τ依赖性可以通过福克-普朗克方程（一种p（x，τ）的广义扩散方程）来描述。该方程完全由两个系数D1（x，τ）和D2（x，τ）（分别为漂移系数和扩散系数）决定。我们演示了如何直接从数据中估计这些系数，而不使用任何假设或模型的基础随机过程。此外，它表明，由此产生的福克-普朗克方程的解决方案正确地描述了经验的pdf，包括明显的尾巴。
We present a stochastic analysis of a data set consisting of 106quotes of the US Dollar–German Mark exchange rate. Evidence is given that the price changes x(τ) upon different delay times τ can be described as a Markov process evolving in τ. Thus, the τ-dependence of the probability density function (pdf) p(x,τ) on the delay time τ can be described by a Fokker–Planck equation, a generalized diffusion equation for p(x,τ). This equation is completely determined by two coefficients D1(x,τ) and D2(x,τ) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker–Planck equation describe the empirical pdfs correctly, including the pronounced tails.