Quantile autoregression neural network model with applications to evaluating value at risk

Abstract

We develop a new quantile autoregression neural network (QARNN) model based on an artificial neuralnetwork architecture. The proposed QARNN model is flexible and can be used to explore potential non-linear relationships among quantiles in time series data. By optimizing an approximate error functionand standard gradient based optimization algorithms, QARNN outputs conditional quantile functionsrecursively. The utility of our new model is illustrated by Monte Carlo simulation studies and empiricalanalyses of three real stock indices from the Hong Kong Hang Seng Index (HSI), the US S&P500 Index(S&P500) and the Financial Times Stock Exchange 100 Index (FTSE100).