Klamut Jarosław, Gubiec Tomasz
Institute of Experimental Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland.
Entropy (Basel). 2021 Nov 26;23(12):1576. doi: 10.3390/e23121576.
In many physical, social, and economic phenomena, we observe changes in a studied quantity only in discrete, irregularly distributed points in time. The stochastic process usually applied to describe this kind of variable is the continuous-time random walk (CTRW). Despite the popularity of these types of stochastic processes and strong empirical motivation, models with a long-term memory within the sequence of time intervals between observations are rare in the physics literature. Here, we fill this gap by introducing a new family of CTRWs. The memory is introduced to the model by assuming that many consecutive time intervals can be the same. Surprisingly, in this process we can observe a slowly decaying nonlinear autocorrelation function without a fat-tailed distribution of time intervals. Our model, applied to high-frequency stock market data, can successfully describe the slope of decay of the nonlinear autocorrelation function of stock market returns. We achieve this result without imposing any dependence between consecutive price changes. This proves the crucial role of inter-event times in the volatility clustering phenomenon observed in all stock markets.
在许多物理、社会和经济现象中，我们观察到所研究数量的变化仅出现在离散的、分布不规则的时间点上。通常用于描述这类变量的随机过程是连续时间随机游走（CTRW）。尽管这类随机过程很受欢迎且有很强的实证动机，但在物理学文献中，在观测时间间隔序列内具有长期记忆的模型却很少见。在这里，我们通过引入一类新的CTRW来填补这一空白。通过假设许多连续的时间间隔可以相同，将记忆引入模型。令人惊讶的是，在这个过程中，我们可以观察到一个缓慢衰减的非线性自相关函数，而时间间隔没有肥尾分布。我们的模型应用于高频股票市场数据时，可以成功描述股票市场回报的非线性自相关函数的衰减斜率。我们在不施加连续价格变化之间任何依赖关系的情况下得到了这个结果。这证明了事件间时间在所有股票市场中观察到的波动聚集现象中的关键作用。
