Approximate Bayesian Computation (ABC) provides Monte Carlo inference of the posterior distribution, even for models with intractable likelihoods. The quality of ABC inference relies on the choice of tolerance for the distance between the observed data summary statistics, and the summary...

The hat matrix maps the vector of response values in a regression to its predicted counterpart. The trace of this hat matrix is the workhorse for calculating the effective number of parameters in both parametric and nonparametric regression settings. Drawing on the regression literature, the...

The asymmetry in the tail dependence between U.S. equity portfolios and the aggregate U.S. market is a well-established property. Given the limited number of observations in the tails of a joint distribution, standard non-parametric measures of tail dependence have poor finite-sample properties...

We derive analytically the first four conditional moments of the integrated variance implied by the GARCH diffusion process. From these moments we obtain an analytical closed-form approximation formula to price European options under the GARCH diffusion model.Using Monte Carlo simulations, we...