Ken West

A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix

This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions. (This abstract was borrowed from another version of this item.)

Automatic Lag Selection in Covariance Matrix Estimation

We propose a nonparametric method for automatically selecting the number of autocovariances to use in computing a heteroskedasticity and autocorrelation consistent covariance matrix. For a given kernel for weighting the autocovariances, we prove that our procedure is asymptotically equivalent to one that is optimal under a mean squared error loss function. Monte Carlo simulations suggest that our procedure performs tolerably well, although it does result in size distortions.

Asymptotic inference about predictive ability

This paper develops procedures for inference about the moments of smooth functions of out-of-sample predictions and prediction errors when there is a long time series of predictions and realizations. The aim is to provide tools for analysis of predictive accuracy and efficiency and, more generally, of predictive ability. The paper allows for nonnested and nonlinear models as well as for possible dependence of predictions and prediction errors on estimated regression parameters. Simulations indicate that the procedures can work well in samples of size typically available. Copyright 1996 by The Econometric Society.

Hypothesis Testing with Efficient Method of Moments Estimation

Efficient method of moments estimation techniques include many commonly used techniques, including ordinary least squares, two- and three-stage least squares, quasi maximum likelihood, and versions of these for nonlinear environments. For models estimated by any efficient method of moments technique, the authors define analogues to the maximum likeliho od based Wald, likelihood ratio, Lagrange multiplier, and minimum chi-squared statistics. They prove the mutual asymptotic equivalence of the four in an environment that allows for disturbances that are auto correlated and heteroskedastic. They also describe a very convenient way to test a linear hypothesis in a linear model. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Bose-Einstein Condensation of Microcavity Polaritons in a Trap

We have created polaritons in a harmonic potential trap analogous to atoms in optical traps. The trap can be loaded by creating polaritons 50 micrometers from its center that are allowed to drift into the trap. When the density of polaritons exceeds a critical threshold, we observe a number of signatures of Bose-Einstein condensation: spectral and spatial narrowing, a peak at zero momentum in the momentum distribution, first-order coherence, and spontaneous linear polarization of the light emission. The polaritons, which are eigenstates of the light-matter system in a microcavity, remain in the strong coupling regime while going through this dynamical phase transition.

A Specification Test for Speculative Bubbles

The set of parameters needed to calculate the expected present discounted value of a stream of dividends can be estimated in two ways. One may test for speculative bubbles, or fads, by testing whether the two estimates are the same. When the test is applied to some annual U.S. stock market data, the data usually reject the null hypothesis of no bubbles. The test is of general interest since it may be applied to a wide class of linear rational expectations models.

Dividend Innovations and Stock Price Volatility

This paper establishes an inequality that may be used to test the null hypothesis that a stock price equals the expected present discounted value of its dividend stream, with a constant discount rate. The inequality states that if this hypothesis is true, the variance of the innovation in the stock price is bounded above by a certain function of the variance in the innovation in the dividend. The bound is valid even if prices and dividends are nonstationary.The inequality is used to test the null hypothesis, for some long term annual U.S. stock price data. The null is decisively rejected, with the stock price innovation variance exceeding its theoretical upper bound by a factor of as much as twenty. The rejection is highly significant statistically. Regression diagnostics and some informal analysis suggest that the results are more consistent with there being speculative bubbles in the U.S. stock market than with a failure of the rational expectations or constant discount rate hypothesis.

The Predictive Ability of Several Models of Exchange Rate Volatility

We compare the out-of-sample forecasting performance of univariate homoskedastic, GARCH, autoregressive and nonparametric models for conditional variances, using five bilateral weekly exchange rates for the dollar, 1973-1989. For a one week horizon, GARCH models tend to make slightly more accurate forecasts. For longer horizons, it is difficult to find grounds for choosing between the various models. None of the models perform well in a conventional test of forecast efficiency.

A utility-based comparison of some models of exchange rate volatility

When estimates of variances are used to make asset allocation decisions, underestimates of population variances lead to lower expected utility than equivalent overestimates: a utility based criterion is asymmetric, unlike standard criteria such as mean squared error. To illustrate how to estimate a utility based criterion, we use five bilateral weekly dollar exchange rates, 1973-1989, and the corresponding pair of Eurodeposit rates. Of homoskedastic, GARCH, autoregressive and nonpararnetric models for the conditional variance of each exchange rate, GARCI-J models tend to produce the highest utility, on average. A mean squared error criterion also favors GARCH, but not as sharply.

Asymptotic Normality, When Regressors Have a Unit Root

Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance-covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero. Copyright 1988 by The Econometric Society.