This paper performs a thorough statistical examination of the time-series properties of the market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies on the widespread consensus that the VIX is a barometer to the overall market sentiment as to what concerns risk appetite. To assess the statistical behavior of the time series, we run a series of preliminary analyses whose results suggest there is some long-range dependence in the VIX index. This is consistent with the strong empirical evidence in the literature supporting long memory in both options-implied and realized volatilities. We thus resort to linear and nonlinear heterogeneous autoregressive (HAR) processes, including smooth transition and threshold HAR-type models, as well as to smooth transition autoregressive trees (START) for modeling and forecasting purposes. The in-sample results for the HAR-type indicate that they cope with the long-range dependence in the VIX time series as well as the more popular ARFIMA model. In addition, the highly nonlinear START specification also does a god job in controlling for the long memory. The out-of-sample analysis evince that the linear ARMA and ARFIMA models perform very well in the short run and very poorly in the long-run, whereas the START model entails by far the best results for the longer horizon despite of failing at shorter horizons. In contrast, the HAR-type models entail reasonable relative performances in most horizons. Finally, we also show how a simple forecast combination brings about great improvements in terms of predictive ability for most horizons.