Non‐Gaussian geostatistical modeling using (skew) t processes

We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with t marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew‐Gaussian process, thus obtaining a process with skew‐t marginal distributions. For the proposed (skew) t process, we study the second‐order and geometrical properties and in the t case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the t process. Moreover we compare the performance of the optimal linear predictor of the t process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia.     

INFORMATION AND THE EQUITY PREMIUM

We determine how better information affects the average equity premium in a standard representative‐agent exchange economy. Perfect information obviously eliminates the equity premium, and a particular kind of information about the level of future consumption always lowers the average equity premium. Surprisingly, information sometimes raises the average equity premium, no matter what the preferences of the representative agent. Information purely about the volatility either of consumption or the marginal utility of consumption raises the equity premium for a wide class of preferences. Moreover, information can raise the average equity premium by an arbitrarily large percentage (while still matching important magnitudes, such as average growth and the risk‐free rate). We consider two different economies: a two‐period economy with arbitrary preferences for the representative agent; and an infinite horizon economy, in which we restrict both preferences and the endowment distribution.     

On Least Absolute Value Estimators for Poisson Processes

We consider the problem of parameter estimation for an inhomogeneous Poisson process observed on the time interval [0, τ]. We introduce the minimum L ₁-norm estimator of the unknown parameter and study the asymptotical behaviors of the estimates when the number of observations increases. It is established that this estimator is consistent and we show that the corresponding differences converge to certain variables. These limit variables are asymptotically normal as τ tends to infinity.