Comparing conditional and stochastic volatility models: goodness of fit, forecasting and value-at-risk

Abstract

In this work a comparison of three families of volatility models, namely the Autoregressive Conditional Heteroskedasticity (ARCH), Stochastic Volatility (SV) and Non-Gaussian State Space Models (NGSSM) is made according to three dierent metrics: goodness of t, forecasting andassessing Value-at-Risk (VaR). Inference procedures under the exible Skew Generalized Error family of distributions is detailed. Respective evaluation criteria used for these metrics are the Akaike Information Criterion, Mean Squared Error of one-step-ahead forecasts and Unconditional Coverage of one-step-ahead VaR. The data used are daily asset return series (Ibovespa, Hang Seng Index, Merval Index and S&PTSX Index) from Jan-2000 to Jan-2016, or roughly 4000 observations,from which 3000 are used for estimation and 1000 are reserved for forecasting and VaR evaluation. Parameter estimates serve as basis to conduct a simulation experiment which consists of 1000 replications of series with the same number of observations for estimation and forecasting as the return data. Simulation results indicate that the Stochastic Volatility model consistently outperforms competingspecications in goodness of t and forecasting, and ranks second (right after the APARCH) in assessing the out-of-sample VaR. Conclusions for the EGARCH and NGSSM are mixed: in goodnessof t performance, the APARCH ranks second, the NGSSM ranks third and the EGARCH ranks last; in forecasting performance, the EGARCH is second, the APARCH third and the NGSSM last; in VaR assessment, the APARCH ranks rst, the EGARCH third and the NGSSM last. CPUtime spent on the estimation of each model is also reported and compared: taking the NGSSM as the benchmark, estimation of the SV model takes about 82 times as long, while APARCH estimationtakes about 4 times and EGARCH estimation about 2 times.