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 introduce firm heterogeneity into the standard monopolistically competitive real business cycle (RBC) model. The fundamental equilibrium path is derived and the time-series properties of aggregate GDP are studied analytically. Although firms' productivities are subject to temporary shocks,...

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...