Research on scaling analysis in finance is vast and still flourishing. We introduce a novel statistical procedure based on the generalized Hurst exponent, the Relative Normalized and Standardized Generalized Hurst Exponent (RNSGHE), to robustly estimate and test the multiscaling property. 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 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 mainly 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.

在金融领域进行规模分析的研究非常广泛且仍在蓬勃发展。我们引入一种基于广义赫斯特指数，相对归一化和标准化广义赫斯特指数（RNSGHE）的新颖统计程序，以稳健地估计和测试多标度属性。此外，我们引入了一种新的工具来估计在我们的方法中使用的最佳聚合时间，我们将该方法称为自相关分段式回归。通过使用多重分形随机游走，我们在模拟的时间序列上对该程序进行了数值验证，然后将其应用于实际财务数据。我们给出了有无异常的时间序列的结果，并计算了这种异常在缩放指数的测量中引入的偏差。我们还展示了如何使用适当的缩放比例和多缩放比例可以改善风险度量（如风险价值（VaR））的估计。最后，我们提出了一种基于蒙特卡洛模拟的方法，该方法被称为多标度风险值（MSVaR），该方法考虑了多标度时间序列的统计属性。我们主要显示，通过结合使用此统计程序和可靠估计的多标度指数，预测一年的MSVaR可以模拟大多数股票年度数据上的VaR。