关于具有长期记忆的时变方差的推广模型
On a generalised model for time-dependent variance with long-term memory
摘要：
该方法（R. F. Engle，1982）构成了具有时变方差的随机时间序列的范例生成器，就像它出现在除了经济学之外的广泛系统中一样。虽然随机过程捕捉到了所谓的“波动性聚集”和随机变量的渐近幂律概率密度分布，但它无法再现许多这些时间序列的进一步统计特性，例如：以Hurst指数的大值为特征的瞬时方差的强持续性（H > 0.8）和绝对值自关联函数的渐近幂律衰减。通过考虑从具有q指数形式的过去收益的相关性获得的有效收益，我们能够修复原始模型的局限性。此外，这种改进可以通过正确选择唯一的附加参数$q_{m}$来获得。通过模拟SP500金融指数的日波动，对其有效性和实用性进行了评估。
英文摘要：
The ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.
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。
