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.
Highlights
The paper proposes a new method of dynamic VaR and CVaR risk measures forecasting
A large number of works devoted to the method of VaR and CVaR estimating based on the stochastic time series model
We propose a new method for VaR and CVaR prediction for financial time series
Summary
Zrazhevska standard measures of market risk management Their popularity has led to a large number of publications on this topic in recent years. Definition, description of the properties and comparative analysis of these risk measures can be found, for example, in [1] [2] [3]. Various methods for their evaluation and forecasting that represents different approaches are proposed. A large number of works devoted to the method of VaR and CVaR estimating based on the stochastic time series model. A significant number of works show the practical application of the approach for estimating and forecasting of stock indices, see for example [10] [11] [12] [13]
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