We provide an in-depth analysis of the theoretical properties of the Hansen-Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. Under a multivariate elliptical distribution assumption, we present explicit expressions for the HJ-distance with a no-arbitrage constraint, the...

Recurrence relations for integrals that involve the density of multivariate normal distributions are developed. These recursions allow fast computation of the moments of folded and truncated multivariate normal distributions. Besides being numerically efficient, the proposed recursions also...

A large number of exact inferential procedures in statistics and econometrics involve the sampling distribution of ratios of random variables. If the denominator variable is positive, then tail probabilities of the ratio can be expressed as those of a suitably defined difference of random...

We present a simple stochastic representation for the joint distribution of sample estimates of three scalar parameters and two vectors of portfolio weights that characterize the minimum-variance frontier. This stochastic representation is useful for sampling observations efficiently, deriving...

This paper considers estimation of moving average (MA) models with non-Gaussian errors. Information in higher-order cumulants allows identification of the parameters without imposing invertibility. By allowing for an unbounded parameter space, the generalized method of moments estimator of the...