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LSTM Mixture Density Networks for Value-at-Risk Forecasting
This Idea covers using a Long Short-Term Memory network with a mixture density output head to forecast Value-at-Risk (VaR) for financial returns. At each time step the LSTM consumes the return history and emits the parameters -- weights, means, variances -- of a Gaussian mixture predictive distribution, and the desired VaR quantile is read off that distribution; the recurrent state is intended to capture volatility clustering the way GARCH does. Learners see how the number of mixture components (two-component, regularized two-component, and three-component variants) trades flexibility against stability, and how such a model is validated by backtesting VaR exceptions for unconditional coverage and independence against benchmarks like historical simulation and GARCH. It also surfaces the method's practical weaknesses: sensitivity to initialization and heavy dependence on training-data volume.