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...

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...

Kernels are typically justified as a smoothing device in nonparametric analysis. We provide alternative interpretations which could lead to the use of asymmetric kernels. We thus derive the class of optimal asymmetric kernels, and analyse its main properties. We illustrate numerically its...

Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not...

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 study the optimal choice of quasi-likelihoods for nearly integrated, possibly non-normal, autoregressive models. It turns out that the two most natural candidate criteria, minimum Mean Squared Error (MSE) and maximum power against the unit root null, give rise to different optimal...

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...

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,...

Suppose we have observations ranging over t=0,1,…T on real net investment, {I_{n,t}}₀^{T}, and on real gross investment, {I_{g,t}}₀^{T}. We derive a method of calculating the depreciation rate for each of the periods {δ_{t}}₁^{T}, and estimating `the' implied net capital stock...