The multivariate split nomal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the prinicpal axis. The paper derives some properties for this distribution, including its moment...

Let {X_{t}} follow a discrete Gaussian Vector Auto-Regression with deterministic components. We derive the exact finite-sample joint Moment Generating Function (MGF) of the quadratic forms that form the basis for the sufficient statistic. The formula is then specialized to the limiting MGF of...

Let {X_{t}} be a discrete multivariate Gaussian autoregressive process of order 1. The paper derives the exact finite-sample joint moment generating function (mgf) of the three quadratic forms constituting the sufficient statistic of the process. The formula is then specialized to some cases of...

We derive the relation between the biases of correlograms and of estimates of auto-regressive AR(k) representations of stationary series, and we illustrate it with a simple AR example. The new relation allows for k to vary with the sample size, which is a representation that can be used for most...