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...

We show that in a purely nonstationary Vector Autoregression (VAR), the biases of Maximum Likelihood and Least Squares Estimators are asymptotically proportional to the dimension of the system, even when the equations and regressors are generated independantly of each other. When some stable...

Ways of improving the efficiency of Monte-Carlo (MC) techniques are studied for dynamic models. Such models cause the conventinal Antithetic Variate (AV) technique to fail, and will be proved to reduce the benefit from using Control Variates with nearly non-stationary series. This paper suggest...

The limiting marginal density of efficient estimators of bivariate cointegration vectors is derived in closed form. The formula is exact, and it consists of highly efficient convergent expansion. It is used to plot the density. Furthermore, it is manipulated analytically to reveal features that...

Hypergeometric functions are a generalization of exponential functions. They are explicit, computable functions that can also be manipulated analytically. The functions and series we use in quantitative economics are all special cases of them. In this paper, a unified approach to hypergeometic...

Two or more variables are said to be cointegrated when they move closely togather over time, after proper scaling. Cointegration was taken to be the statistical expression of the notion of equilibrium in economics. But is it still possible to talk of cointegration when "disequilibrium" economics...

Hypergeometric functions are a generalization of exponential functions. They are explicit, computable functions that can also be manipulated analytically. The functions and series we use in quantitative economics are all special cases of them. In this paper, a unified approach to hypergeometric...