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 analyse the scaling properties of time series is through the estimation of scaling exponents. These exponents are recognized as being valuable measures to discriminate between random, persistent, and anti-persistent behaviours in time series. In the literature, several methods have been proposed to study the multiscaling property and in this paper we use the generalized Hurst exponent (GHE) . On the base of this methodology, we propose a novel statistical procedure  to robustly estimate and test the multiscaling property and we name it RNSGHE. This methodology , together with a combination of t-tests and F-tests to discriminated between real and spurious scaling. Moreover, we also introduce a new methodology to estimate the optimal aggregation time used in our methodology  . We numerically validate our procedure on simulated time series  using the Multifractal Random Walk (MRW) and  then apply it to real financial data. We also 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. Finally, we show how the use of proper scaling and multiscaling can ameliorate the estimation of risk measures such as Value at Risk (VaR). We also propose a methodology based on Monte Carlo simulation, that we name Multiscaling Value at Risk (MSVaR), which takes into account the statical 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 analysed .
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 .
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