This paper represents a pioneering effort to investigate multifractal dynamics that exclusively encompass the return time series of USA Education Group Stocks concerning two non-overlapping periods (before, during, and after COVID-19). Given this, we employ the Multifractal Detrended Fluctuations Analysis (MF-DFA). In this sense, we investigate the generalized Hurst exponent $h(q)$ and the Rényi exponent $\tau (q)$ for each asset and quantify their statistical properties, which allowed us to observe separately the contributing small scale (primarily via the negative moments $q$) and the large scale (via the positive moments $q$). We perform a fourth-degree polynomial regression fit to estimate the complexity parameters that describe the degree of multifractality of the underlying process. Also, we shall apply the inefficiency multifractal index to assess the COVID-19 shock for both periods. Our findings show that for both periods, the majority of these assets are marked by multifractal dynamics associated with persistent behavior $({\alpha }_0>0.5)$, a higher degree of multifractality and the dominance of large fluctuations. At the same time, most of these assets show asymmetry parameter $(R>1)$ for both periods, indicating that large fluctuations contributed more to multifractality in the time series of returns.

本文代表了研究多重分形动力学的开创性努力，该动力学专门包含美国教育集团股票关于两个非重叠时期（COVID-19 之前、期间和之后）的回报时间序列。鉴于此，我们采用多重分形去趋势波动分析 (MF-DFA)。从这个意义上说，我们研究广义赫斯特指数$H（q）$和 Rényi 指数$\tau （q）$对于每项资产并量化其统计属性，这使我们能够单独观察贡献的小规模（主要通过负矩$q$）和大规模（通过积极的时刻$q$）。我们执行四次多项式回归拟合来估计描述基础过程的多重分形程度的复杂性参数。此外，我们将应用无效率多重分形指数来评估这两个时期的 COVID-19 冲击。我们的研究结果表明，在这两个时期，大多数资产都以与持久行为相关的多重分形动态为特征$（{\alpha }_0>0。5）$，较高程度的多重分形和大波动的主导地位。同时，这些资产大多表现出参数不对称性$（右>1）$对于这两个时期，表明较大的波动对回报时间序列的多重分形贡献更大。