  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.
