金融市场的波动性、持续性与生存
Volatility, Persistence, and Survival in Financial Markets
摘要：
我们使用非平衡统计力学的一般技术和方法，研究时间依赖的股票价格（包括个人和复合）的时间波动作为一种随机现象。特别是，我们分析股票价格波动作为一个非马尔可夫随机过程，使用的第一次通过统计概念的持久性和生存。我们报告的实证测量结果的归一化$q$阶相关函数$f_q(t)$，生存概率$S(t)$，和持久性概率$P(t)$几个股票市场动态集。我们分析每分钟和更高频率的股票市场记录（即，采样时间$δt$为几天）。我们发现，波动的股票价格是多重分形和$δt$的选择没有影响的定性多重分形行为所显示的$1/q$依赖的广义赫斯特指数$H_q$与幂律演化的相关函数$f_q(t)\sim t^{H_q}$。股票价格在时间$t$之前保持高于平均值的概率$S(t)$对总测量时间$t_m$和采样时间非常敏感。股票在$t$区间内不返回到初始值的概率$P(t)$具有普适幂律行为$P(t)\sim t^{-θ}$，持续指数$θ$接近0.5，与预测$θ=1-H_2$一致。经验金融股票也提出了一个有趣的功能，发现在湍流，扩展自相似性。
英文摘要：
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price fluctuations as a non-Markovian stochastic process using the first-passage statistical concepts of persistence and survival. We report the results of empirical measurements of the normalized $q$-order correlation functions $f_q(t)$, survival probability $S(t)$, and persistence probability $P(t)$ for several stock market dynamical sets. We analyze both minute-to-minute and higher frequency stock market recordings (i.e., with the sampling time $δt$ of the order of days). We find that the fluctuating stock price is multifractal and the choice of $δt$ has no effect on the qualitative multifractal behavior displayed by the $1/q$-dependence of the generalized Hurst exponent $H_q$ associated with the power-law evolution of the correlation function $f_q(t)\sim t^{H_q}$. The probability $S(t)$ of the stock price remaining above the average up to time $t$ is very sensitive to the total measurement time $t_m$ and the sampling time. The probability $P(t)$ of the stock not returning to the initial value within an interval $t$ has a universal power-law behavior, $P(t)\sim t^{-θ}$, with a persistence exponent $θ$ close to 0.5 that agrees with the prediction $θ=1-H_2$. The empirical financial stocks also present an interesting feature found in turbulent fluids, the extended self-similarity.
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