Anil K. Bera

Efficient tests for normality, homoscedasticity and serial independence of regression residuals

We use the Lagrange multiplier procedure to derive efficient joint tests for residual normality, homoscedasticity and serial independence. The tests are simple to compute and asymptotically distributed as χ2.

A Test for Normality of Observations and Regression Residuals

Summary Using the Lagrange multiplier procedure or score test on the Pearson family of distributions we obtain tests for normality of observations and regression disturbances. The tests suggested have optimum asymptotic power properties and good finite sample performance. Due to their simplicity they should prove to be useful tools in statistical analysis.

Simple diagnostic tests for spatial dependence

In this paper we propose simple diagnostic tests, based on ordinary least-squares (OLS) residuals, for spatial error autocorrelation in the presence of a spatially lagged dependent variable and for spatial lag dependence in the presence of spatial error autocorrelation, applying the modified Lagrange multiplier (LM) test developed by Bera and Yoon (Econometric Theory, 1993, 9, 649-658). Our new tests may be viewed as computationally simple and robust alternatives to some existing procedures in spatial econometrics. We provide empirical illustrations to demonstrate the usefulness of the proposed tests. The finite sample size and power performance of the tests are also investigated through a Monte Carlo study. The results indicate that the adjusted LM tests have good finite sample properties. In addition, they prove to be more suitable for the identification of the source of dependence (lag or error) than their unadjusted counterparts.

A CLASS OF NONLINEAR ARCH MODELS

A class of nonlinear autoregressive conditional heteroskedasticity models is suggested. The proposed class encompasses several functional forms for autoregressive conditional heteroskedasticity which have been put forth in the literature. A Lagrange multiplier test is developed to test Engles autoregressive conditional heteroskedasticity specification against the wider class of models. This test provides an easily computed disgnostic check of the adequacy of an autoregressive conditional heteroskedasticity model after it has been estimated. The theory is applied to a number of weekly exchange rate series and the authors find strong evidence of nonlinear autoregressive conditional heteroskedasticity. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo Evidence

Abstract In this paper we study the performance of various tests for normality (N), homoscedasticity (H) and serial independence (I) of regression residuals (u) under one, two and three directional departures from HO:u∼NHI.

Model specification tests: A simultaneous approach

Abstract In econometrics, specification tests have been constructed to verify the validity of one specification at a time. It is argued that most of these tests are not, in general, robust in the presence of other misspecifications, so their application may result in misleading conclusions. Using the Lagrange Multiplier principle we develop efficient test procedures that are capable of testing a number of specifications simultaneously. These tests will ‘confirm’ the validity (or invalidity) of a general model requiring the estimates of the restricted model only. Through an extensive Monte Carlo experiment we study the performance of these tests and some commonly used one-directional tests. We also suggest a Multiple Comparison Procedure, to identify different sources of errors. This, we hope, will lead to a better specification of econometric models.

SPECIFICATION TESTING WITH LOCALLY MISSPECIFIED ALTERNATIVES

It is well known that most of the standard specification tests are not robust when the alternative is misspecified. Using the asymptotic distributions of standard Lagrange multiplier (LM) test under local misspecification, we suggest a robust specification test. This test essentially adjusts the mean and covariance matrix of the usual LM statistic. We show that for local misspecification the adjusted test is asymptotically equivalent to Neymans C(I±) test, and therefore, shares the optimality properties of the C(I±) test. The main advantage of the new test is that, compared to the C(I±) test, it is much simpler to compute. Our procedure does require full specification of the model and there might be some loss of asymptotic power relative to the unadjusted test if the model is indeed correctly specified.

Testing Constancy of Correlation and Other Specifications of the BGARCH Model with an Application to International Equity Returns

One of the main ingredients in forming an international portfolio is the correlation matrix. The correlations represent the degree of interdependence across markets. With the recent globalization of markets and increased volatility, we can expect these correlations to change over time, and quite possibly to go up. However, the standard practice in modeling asset return dynamics is to assume constant correlation. This parameterization is simple, and it involves a relatively small number of parameters. However, the validity of this assumption remains an empirical question. This paper is concerned with developing a formal test for constancy of correlation, and applying it to financial markets of the USA, Japan, Germany, the UK, France and Italy.

Rao's score, Neyman's C(α) and Silvey's LM tests: an essay on historical developments and some new results

Abstract Raos (Proc. Cambridge Philos. Soc. 44 (1948a) 50) seminal paper introduced a fundamental principle of testing based on the score function as an alternative to likelihood ratio and Wald tests. Neymans (In: Grenander, (Ed.), Probability and Statistics, the Harald Cramer Volume, Almqvist and Wiksell, Uppsala, pp. 213–234) approach, in view of the presence of nuisance parameters, emphasized the generality and attractive features of the score-based tests. Silvey (Ann. Math. Statist. 30 (1959) 389) rediscovered the score test as a Lagrange multiplier test. Breusch and Pagans (Rev. Econom. Stud. 47 (1980) 239) exposition of the score test in a general framework in the context of econometric modeling resulted in an increased activity on specification testing in econometrics. In this paper we trace these historical developments emphasizing the optimality features of tests based on scores and their usefulness in practical problems in statistics and econometrics. In so doing we give some new results, present easier computation of score-based tests and alternative derivations of some known results. We also discuss a connection between Raos score test and the seemingly unrelated literature of Fishers discriminant function, Mahalanobis’ D 2 and Hotellings T 2 .

FURTHER EVIDENCE ON ASYMPTOTIC TESTS FOR HOMOGENEITY AND SYMMETRY IN LARGE DEMAND SYSTEMS

Abstract The asymptotically equivalent Lagrange multiplier, likelihood ratio and Wald tests are compared when testing for homogeneity and symmetry. The need for size correction becomes apparent as does the superior performance of the LM test under H 0 .