Halbert White

A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity

This paper presents a parameter covariance matrix estimator which is consistent even when the disturbances of a linear regression model are heteroskedastic. This estimator does not depend on a formal model of the structure of the heteroskedasticity. By comparing the elements of the new estimator to those of the usual covariance estimator, one obtains a direct test for heteroskedasticity, since in the absence of heteroskedasticity, the two estimators will be approximately equal, but will generally diverge otherwise. The test has an appealing least squares interpretation.

Multilayer feedforward networks are universal approximators

Abstract This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.

Maximum Likelihood Estimation of Misspecified Models

This paper examines the consequences and detection of model misspecification when using maximum likelihood techniques for estimation and inference. The quasi-maximum likelihood estimator (QMLE) converges to a well defined limit, and may or may not be consistent for particular parameters of interest. Standard tests (Wald, Lagrange Multiplier, or Likelihood Ratio) are invalid in the presence of misspecification, but more general statistics are given which allow inferences to be drawn robustly. The properties of the QMLE and the information matrix are exploited to yield several useful tests for model misspecification.

Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks

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A Reality Check for Data Snooping

Data snooping occurs when a given set of data is used more than once for purposes of inference or model selection. When such data reuse occurs, there is always the possibility that any satisfactory results obtained may simply be due to chance rather than to any merit inherent in the method yielding the results. This problem is practically unavoidable in the analysis of time-series data, as typically only a single history measuring a given phenomenon of interest is available for analysis. It is widely acknowledged by empirical researchers that data snooping is a dangerous practice to be avoided, but in fact it is endemic. The main problem has been a lack of sufficiently simple practical methods capable of assessing the potential dangers of data snooping in a given situation. Our purpose here is to provide such methods by specifying a straightforward procedure for testing the null hypothesis that the best model encountered in a specification search has no predictive superiority over a given benchmark model. This permits data snooping to be undertaken with some degree of confidence that one will not mistake results that could have been generated by chance for genuinely good results.

Tests of Conditional Predictive Ability

We argue that the current framework for predictive ability testing (e.g., West, 1996) is not necessarily useful for real-time forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for out-of-sample comparison of predictive ability which delivers more practically relevant conclusions. Our approach is based on inference about conditional expectations of forecasts and forecast errors rather than the unconditional expectations that are the focus of the existing literature. We capture important determinants of forecast performance that are neglected in the existing literature by evaluating what we call the forecasting method (the model and the parameter estimation procedure), rather than just the forecasting model. Compared to previous approaches, our tests are valid under more general data assumptions (heterogeneity rather than stationarity) and estimation methods, and they can handle comparison of both nested and non-nested models, which is not currently possible. To illustrate the usefulness of the proposed tests, we compare the forecast performance of three leading parameter-reduction methods for macroeconomic forecasting using a large number of predictors: a sequential model selection approach, the diffusion indexes approach of Stock and Watson (2002), and the use of Bayesian shrinkage estimators.

Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties

We examine several modified versions of the heteroskedasticity-consistent covariance matrix estimator of Hinkley and White. On the basis of sampling experiments which compare the performance of quasi t statistics, we find that one estimator, based on the jackknife, performs better in small samples than the rest. We also examine finite-sample properties using modified critical values based on Edgeworth approximations, as proposed by Rothenberg. In addition, we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity-consistent covariance matrix even in the absence of detected heteroskedasticity.

Learning in Artificial Neural Networks: A Statistical Perspective

The premise of this article is that learning procedures used to train artificial neural networks are inherently statistical techniques. It follows that statistical theory can provide considerable insight into the properties, advantages, and disadvantages of different network learning methods. We review concepts and analytical results from the literatures of mathematical statistics, econometrics, systems identification, and optimization theory relevant to the analysis of learning in artificial neural networks. Because of the considerable variety of available learning procedures and necessary limitations of space, we cannot provide a comprehensive treatment. Our focus is primarily on learning procedures for feedforward networks. However, many of the concepts and issues arising in this framework are also quite broadly relevant to other network learning paradigms. In addition to providing useful insights, the material reviewed here suggests some potentially useful new training methods for artificial neural networks.

Data-Snooping, Technical Trading Rule Performance, and the Bootstrap

In this paper we utilize Whites Reality Check bootstrap methodology (White (1997)) to evaluate simple technical trading rules while quantifying the data-snooping bias and fully adjusting for its effect inthe context of the full universe form which the trading rules are drawn. Henxe, for the first time, the paper presents a comrehensive test of perfomance across all technical trading rules examined. We consider the study of brock, Lakonishok and LeBaron (1992), expand their universe of 26 trading rules, apply the rules to 100 years of daily data on the Dow Jone Industrial Average, and determine the effects of data-snooping.

Can Mutual Fund 'Stars' Really Pick Stocks? New Evidence from a Bootstrap Analysis

We apply an innovative bootstrap statistical technique to examine the performance of the U.S. equity mutual fund industry during the 1962 to 1994 period. Using this new method, we bootstrap the distribution of the performance measure (the “alpha”) across mutual funds to determine whether funds with the best alphas are simply lucky, or whether managers of these funds possess genuine stockpicking skills—this bootstrap technique is necessary because of the complicated form of the distribution of alphas across funds and the non-normal nature of individual funds’ alphas. Our results indicate that, controlling for luck, fund managers that pick stocks well enough to more than cover their costs do exist. That is, the distribution of alphas computed from bootstrapped fund returns (and assuming that no stockpicking talent exists) has a much smaller right tail than the distribution of alphas computed from actual fund returns. Unfortunately for investors, our bootstrap results also show strong evidence of funds with significant inferior performance. Further, our evidence suggests that stockpicking skills are most clearly evident among growth-fund managers. In general, our study supports the value of active mutual fund management, although it also highlights the drawbacks of funds actively managed by those who cannot pick stocks.