The information contents of vix index and range-based volatility on volatility forecasting performance of s&p 500

In this paper, we investigate the information contents of S&P 500 VIX index and range-based volatilities by comparing their benefits on the GJR-based volatility forecasting performance. To reveal the statistical significance and ensure obtaining robust results, we employ Hansen's SPA test (2005) to examine the forecasting performances of GJR and GJR-X models for the S&P500 stock index. The results indicate that combining VIX and range-based volatilities into GARCH-type model can both enhance the one-step-ahead volatility forecasts while evaluating with different kinds of loss functions. Moreover, regardless of under-prediction, GJR-VIX model appears to be the most preferred, which implies that VIX index has better information content for improving volatility forecasting performance.Range-based volatilities; GJR-based volatility forecasting; VIX index; SPA test

Frequently Hypercyclic and Chaotic Behavior of Some First-Order Partial Differential Equation

We study a particular first-order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup. Furthermore, we show that it satisfies the frequently hypercyclic criterion, and hence the solution semigroup is also a chaotic semigroup