a b s t r a c tThe new distribution class, Asymmetric Exponential Power Distribution (AEPD), proposed in this paper generalizes the class of Skewed Exponential Power Distributions (SEPD) in a way that in addition to skewness introduces different decay rates of density in the left and right tails. Our parametrization provides an interpretable role for each parameter. We derive moments and moment-based measures: skewness, kurtosis, expected shortfall. It is demonstrated that a maximum entropy property holds for the AEPD distributions. We establish consistency, asymptotic normality and efficiency of the maximum likelihood estimators over a large part of the parameter space by dealing with the problems created by non-smooth likelihood function and derive explicit analytical expressions of the asymptotic covariance matrix; where the results apply to the SEPD class they enlarge on the current literature. Also we give a convenient stochastic representation of the distribution; our Monte Carlo study illustrates the theoretical results. We also provide some empirical evidence for the usefulness of employing AEPD errors in GARCH type models for predicting downside market risk of financial assets.

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on "identification at infinity" which leads to non-standard convergence rate. Andrews and Schafgans (1998) derived asymptotic results for a smoothed version of the estimator. We examine the optimal bandwidth selection for the estimators and derive asymptotic MSE rates under a wide class of distributional assumptions. We also provide some comparisons of the estimators and practical guidelines.

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We examine a simple estimator for the multivariate moving average model based on vector autoregressive approximation. In nite samples the estimator has a bias which i s low where roots of the determinantal equation are w ell away from the unit circle, and more substantial where one or more roots have m odulus near unity. W e s h ow that the representation estimated by this m ultivariate technique is consistent a n d asymptotically invertible. This estimator has signicant computational advantages over Maximum Likelihood, a n d more importantly may be more r obust than ML to mis-specication o f t h e v ector moving average model. The estimation method is a p plied to a VMA model of wholesale and retail inventories, using Canadian data on overall aggregate, non-durable a n d d u rable inventory investment, and a l lows us to examine the propagation of shocks between the two classes of inventory.

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