The contour map of estimation error of Expected Shortfall (ES) is constructed. It allows one to quantitatively determine the sample size (the length of the time series) required by the optimization under ES of large institutional portfolios for a given size of the portfolio, at a given...

This chapter summarizes recent literature on asymptotic inference about forecasts. Both analytical and simulation based methods are discussed. The emphasis is on techniques applicable when the number of competing models is small. Techniques applicable when a large number of models is compared to...

How frequent are large disagreements in human judgment? The substantial literature relating to expert assessments of real-valued quantities and their aggregation almost universally assumes that errors follow a jointly normal distribution. We investigate this question empirically using 17...

This paper conducts a comprehensive investigation of the "forecast combination puzzle" in the context of the heterogeneous autoregressive (HAR) model for volatility forecasting. The widely-used HAR model can be considered as a theoretically optimal combination of three random-walk forecasts...