Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 001

IRTG 1792 Discussion Paper 2018-001

Data Driven Value-at-Risk Forecasting using a SVR-GARCH-KDE Hybrid

Marius Lux
Wolfgang Karl Härdle
Stefan Lessmann

Appropriate risk management is crucial to ensure the competitiveness of financial institutions
and the stability of the economy. One widely used financial risk measure is Value-at-Risk
(VaR). VaR estimates based on linear and parametric models can lead to biased results or
even underestimation of risk due to time varying volatility, skewness and leptokurtosis of
nancial return series. The paper proposes a nonlinear and nonparametric framework to
forecast VaR. Mean and volatility are modeled via support vector regression (SVR) where
the volatility model is motivated by the standard generalized autoregressive conditional
heteroscedasticity (GARCH) formulation. Based on this, VaR is derived by applying kernel
density estimation (KDE). This approach allows for exible tail shapes of the profit and loss
distribution and adapts for a wide class of tail events.
The SVR-GARCH-KDE hybrid is compared to standard, exponential and threshold
GARCH models coupled with different error distributions. To examine the performance in
different markets, one-day-ahead forecasts are produced for different financial indices. Model
evaluation using a likelihood ratio based test framework for interval forecasts indicates that
the SVR-GARCH-KDE hybrid performs competitive to benchmark models. Especially models
that are coupled with a normal distribution are systematically outperformed.

Keywords: Value-at-Risk, Support Vector Regression, Kernel Density Estimation, GARCH