Computationally Efficient Bootstrap Prediction Intervals for Returns and Volatilities in ARCH and GARCH Processes

We propose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box–Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the nonlinear GARCH framework. Our simulation studies indicate that the new re-sampling method provides sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs by up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by an application to Yen/U.S. dollar daily exchange rate data.

Do Colombian students underestimate higher education returns?

We analyze the determinants of subjective returns of higher education in Colombia. The information on expectations has been collected in categories, motivating the use of interval regression and an ordered probit approaches for modeling the relationship between beliefs and measures of ability, conditioning on individual, school and regional covariates. The results suggest that there are considerable differences in the size of the expected returns according to some population groups and a strong dominance of college against technical education. Gender gaps disappear in college education but it is found that girls tend to believe that professional wages are more concentrated into higher income categories than boys. Finally, it seems that Colombian students overestimate the pecuniary returns to education.