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arXiv 1701.01255q-fin.STphysics.soc-ph
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作为金融市场长期记忆实证检验的突发和突发间持续时间统计

Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets

V. Gontis, A. Kononovicius

摘要:

我们讨论了金融市场中的长程记忆问题。有两种概念上不同的方法来再现自相关函数的幂律衰减:使用分数布朗运动以及非线性随机微分方程。在这篇文章中,我们通过分析外汇市场的经验回报和交易活动时间序列来解决这个问题。从经验时间序列中,我们得到了突发和突发间持续时间的概率密度函数。我们的分析表明,所获得的概率密度函数的幂律指数接近$3/2$,这是一维随机过程的一个特征。这是在一个很好的协议与早期提出的绝对回报模型的基础上的非线性随机微分方程推导出的基于代理人的羊群模型。

英文摘要:

We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing empirical return and trading activity time series from the Forex. From the empirical time series we obtain probability density functions of burst and inter-burst duration. Our analysis reveals that the power-law exponents of the obtained probability density functions are close to $3/2$, which is a characteristic feature of the one-dimensional stochastic processes. This is in a good agreement with earlier proposed model of absolute return based on the non-linear stochastic differential equations derived from the agent-based herding model.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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