Data-Driven Adaptive Regularized Risk Forecasting

Regularization methods allow data scientists and risk managers to enhance the predictive power of a statistical model and improve the quality of risk forecasts. Financial risk forecasting is about forecasting volatility, Value at Risk (VaR), expected shortfall (ES) and model risk ratio. While regularized estimates have been shown to perform well in model selection and parameter estimation, their applications in financial risk forecasting has not yet been studied. In this paper, regularized adaptive forecasts and computationally efficient forecasting algorithms for volatility, VaR, ES and model risk are studied using various regularization methods such as ridge, lasso and elastic net. Sample sign correlation of standardized log returns (standardized by volatility forecasts) is used to identify the conditional distribution of the log returns series and provide regularized interval forecasts as well as regularized probability forecasts. Superiority of the regularized risk forecasts is demonstrated using different volatility models including a recently proposed generalized data-driven volatility model in [8]. Validation of the regularized risk forecasts using real financial data is given. Regularized probabilistic forecasts for stationary time series models are also discussed in some detail.