TITLE:
Method of Dynamic VaR and CVaR Risk Measures Forecasting for Long Range Dependent Time Series on the Base of the Heteroscedastic Model
AUTHORS:
Nataliya D. Pankratova, Nataliia G. Zrazhevska
KEYWORDS:
Dynamic VaR, CVaR, Forecasting, Long Range Dependence, Hurst Parameter, Heteroscedastic Model
JOURNAL NAME:
Intelligent Control and Automation,
Vol.8 No.2,
May
26,
2017
ABSTRACT: The
paper proposes a new method of dynamic VaR and CVaR risk measures forecasting.
The method is designed for obtaining the forecast estimates of risk measures
for volatile time series with long range dependence. The method is based on the
heteroskedastic time series model. The FIGARCH model is used for volatility
modeling and forecasting. The model is reduced to the AR model of infinite
order. The reduced system of Yule-Walker equations is solved to find the
autoregression coefficients. The regression equation for the autocorrelation
function based on the definition of a long-range dependence is used to get the autocorrelation
estimates. An optimization procedure is proposed to specify the estimates of
autocorrelation coefficients. The procedure for obtaining of the forecast
values of dynamic risk measures VaR and CVaR is formalized as a multi-step
algorithm. The algorithm includes the following steps: autoregression
forecasting, innovation highlighting, obtaining of the assessments for static
risk measures for residuals of the model, forming of the final forecast using
the proposed formulas, quality analysis of the results. The proposed method is
applied to the time series of the index of the Tokyo stock exchange. The
quality analysis using various tests is conducted and confirmed the high
quality of the obtained estimates.