论文标题
关于缩放指数的统计数据和风险的多标记价值
On the statistics of scaling exponents and the Multiscaling Value at Risk
论文作者
论文摘要
在文献中已经广泛研究了扩展和多标准财务时间序列。关于这个主题的研究是广泛的,仍然蓬勃发展。分析时间序列的缩放属性的一种方法是通过估计其缩放指数,这些缩放指数被认为是在这些时间序列中区分随机,持久性和反性行为的有价值的措施。在文献中,已经提出了几种研究多标准特性的方法。在本文中,我们使用广义Hurst指数(GHE)工具,并提出了一种基于GHE的新统计程序,我们将相对标准化和标准化的广义Hurst指数(RNSGHE)命名。该方法用于稳健地估计和测试多标准属性,并与t检验和f检验的组合结合在一起,可区分真实和虚假缩放。此外,我们引入了一种新工具,以估计方法中使用的最佳聚合时间,我们将自动相关分段的回归命名。我们通过使用多型随机步行(MRW)在模拟时间序列上数字验证此过程,然后将其应用于真实的财务数据。我们提出了有或没有异常的时间序列的结果,并计算了这种异常在测量缩放指数中引入的偏差。我们还展示了适当的缩放和多标准的使用如何改善风险度量等风险量的估计(VAR)。最后,我们提出了一种基于蒙特卡洛模拟的方法,我们将其命名为有风险的多标准值(MSVAR),该方法考虑了多标准时间序列的统计属性。我们表明,通过将此统计程序与可靠的估计多标准指数结合使用,一年预测了MSVAR模仿了所分析的大多数股票的年度数据中的VAR。
Scaling and multiscaling financial time series have been widely studied in the literature. The research on this topic is vast and still flourishing. One way to analyze the scaling properties of time series is through the estimation of their scaling exponents, that are recognized as being valuable measures to discriminate between random, persistent, and anti-persistent behaviors in these time series. In the literature, several methods have been proposed to study the multiscaling property. In this paper, we use the generalized Hurst exponent (GHE) tool and we propose a novel statistical procedure based on GHE which we name Relative Normalized and Standardized Generalized Hurst Exponent (RNSGHE). This method is used to robustly estimate and test the multiscaling property and, together with a combination of t-tests and F-tests, serves to discriminate between real and spurious scaling. Furthermore, we introduce a new tool to estimate the optimal aggregation time used in our methodology which we name Autocororrelation Segmented Regression. We numerically validate this procedure on simulated time series by using the Multifractal Random Walk (MRW) and we then apply it to real financial data. We present results for times series with and without anomalies and we compute the bias that such anomalies introduce in the measurement of the scaling exponents. We also show how the use of proper scaling and multiscaling can ameliorate the estimation of risk measures such as Value at Risk (VaR). Finally, we propose a methodology based on Monte Carlo simulation, which we name Multiscaling Value at Risk (MSVaR), that takes into account the statistical properties of multiscaling time series. We show that by using this statistical procedure in combination with the robustly estimated multiscaling exponents, the one year forecasted MSVaR mimics the VaR on the annual data for the majority of the stocks analyzed.