Gauss' 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss' arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive...

Let Xt be a discrete multivariate autoregressive process of order 1. The paper derives the joint moment generating function (mgf) of the two quadratic forms that are used to define statistics relating to the parameters of this process. The formula is then specialized to some cases of interest,...

In time series containing an autoregressive unit root, almost all known statistics can be described in terms of two Wiener functionals. It is therefore crucial for us to know how these functionals are jointly distributed in terms of explicit formulae that can be manipulated analytically, that do...

Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We show that, with...

We show that the bias of estimated parameters in autoregressive models can increase as the sample size grows. This unusual result is due to the effect of the initial sample observations that are typically neglected in theoretical asymptotoc analysis, in spite of their empirical relevance....

Testing for cointegration is now widespread in economics. Although the principle is sound, the practice has not always been so. In this note, an attempt is made to reveal flaws in some applied testing procedures. Incomplete nonstationary-null procedures make cointegration seem more likely than...