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

Optimal experimental designs for fMRI via circulant biased weighing designs

Functional magnetic resonance imaging (fMRI) technology is popularly used in many fields for studying how the brain reacts to mental stimuli. The identification of optimal fMRI experimental designs is crucial for rendering precise statistical inference on brain functions, but research on this topic is very lacking. We develop a general theory to guide the selection of fMRI designs for estimating a hemodynamic response function (HRF) that models the effect over time of the mental stimulus, and for studying the comparison of two HRFs. We provide a useful connection between fMRI designs and circulant biased weighing designs, establish the statistical optimality of some well-known fMRI designs and identify several new classes of fMRI designs. Construction methods of high-quality fMRI designs are also given.Comment: Published at http://dx.doi.org/10.1214/15-AOS1352 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org