The Finite-Sample E ects of VAR Dimensions on OLS Bias, OLS Variance, and Minimum MSE Estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the nite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary rst-order VAR. Speci cally, we use Monte Carlo simulation and numerical optimization to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct speci cation and several types of over-parameterization of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain minimum mean squared error (MSE). Our results improve and extend one of the main nite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis (Econometrica 67 (1999) 163), generalize the univariate variance and MSE ndings of Abadir (Economics Letters 47 (1995) 263) to the multivariate setting, and complement various asymptotic studies.Finite-sample bias, Monte Carlo simulation, nonstationary time series, response surfaces, vector autoregression.

The finite-sample effects of VAR dimensions on OLS bias, OLS variance, and minimum MSE estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies

Cliques and a new measure of clustering: with application to U.S. domestic airlines

18 pages, 12 figuresWe propose a natural generalization of the well-known clustering coefficient for triples $C(3)$ to any number of nodes. We give analytic formulae for the special cases of three, four, and five nodes and show, using data on U.S. airline networks, that they have very fast runtime performance. We discuss theoretical properties and limitations of the new measure, and use it to provide insight into changes in network structure over time