Forecasting volatility by means of threshold models

The aim of this paper is to compare the forecasting performance of competing threshold models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out-of-sample forecasting ability of the SETAR-Threshold GARCH (SETAR-TGARCH) and the SETAR-Threshold Stochastic Volatility (SETAR-THSV) models compared to the GARCH model and Stochastic Volatility (SV) model. However, the main problem in evaluating the predictive ability of volatility models is that the ‘true’ underlying volatility process is not observable and thus a proxy must be defined for the unobservable volatility. For the class of nonlinear state space models (SETAR-THSV and SV), a modified version of the SIR algorithm has been used to estimate the unknown parameters. The forecasting performance of competing models has been compared for two return time series: IBEX 35 and S&P 500. We explore whether the increase in the complexity of the model implies that its forecasting ability improves.