Testing for serial correlation in the presence of dynamic heteroscedasticity

A recent article in this journal by Tabak (2006) highlighted a potentially serious source of bias that can arise when multiple statistical tests of a damages theory are performed and even one test rejecting the null hypothesis is regarded as supporting the damages theory. Repeated testing will eventually produce a “false discovery,” that is, rejection of the null hypothesis in favor of the alternative hypothesis when the null hypothesis is true, which statisticians refer to as type I error. Consequently, performing multiple tests without adjusting the critical value can be problematical because it can lead to improperly accepting statistical evidence that apparently supports rejection of the null hypothesis as reliable when it is not. Tabak (2006) recommends making the Sidak (1968, 1971) multiple-comparison adjustment to the standard statistical t-test to correct for the false-discovery bias inherent in multiple-comparison testing. In particular, he recommends making this adjustment when performing 10b-5 securities fraud event studies when more than one corrective disclosure date is involved. This article clarifies the circumstances in which a multiple-comparison adjustment is appropriate and explains why the correction is normally not needed in securities fraud event-study testing. More generally, I explain why it is not required when each of several tests is performed and its results are reported separately, as for example, where the objective is simply to test the statistical significance of the abnormal stock return on each day on which a new and distinct curative disclosure occurred. I show that the Sidak multiple-comparison adjustment is nearly as stringent as the classical Bonferroni procedure (Simes, 1986), which can increase the risk of type II error. This article discusses a more powerful alternative to the Sidak adjustment due to Benjamini and Hochberg (1993), which directly corrects for the false-discovery bias in multiple-comparison testing and reduces the risk of type II error. II. Application of Multiple-Comparison Adjustments to Securities Fraud Event Studies Multiple-comparison-false-discovery bias can arise when (a) several statistical tests are performed on subsets of the same larger data set in an effort to

The author considers serial correlation testing in seasonal time series models. He proposes a test statistic based on a spectral approach. Many tests of this type rely on kernel‐based spectral density estimators that assign larger weights to low order lags than to high ones. Under seasonality, however, large autocorrelations may occur at seasonal lags that classical kernel estimators cannot take into account. The author thus proposes a test statistic that relies on the spectral density estimator of Shin (2004), whose weighting scheme is more adapted to this context. The distribution of his test statistic is derived under the null hypothesis and he studies its behaviour under fixed and local alternatives. He establishes the consistency of the test under a general fixed alternative. He also makes recommendations for the choice of the smoothing parameters. His simulation results suggest that his test is more powerful against seasonality than alternative procedures based on classical weighting schemes. He illustrates his procedure with monthly statistics on employment among young Americans.

Hypothesis tests

Journal Article The Determinants of Equilibrium Unemployment in Britain: A Reply Get access S. J. Nickell S. J. Nickell Centre for Labour Economics, London Search for other works by this author on: Oxford Academic Google Scholar The Economic Journal, Volume 95, Issue 377, 1 March 1985, Pages 196–198, https://doi.org/10.2307/2233480 Published: 01 March 1985

Specification Tests for Spatial Panel Data Models

This paper surveys alternative testing criteria in the linear multivariate regression model, and investigates the possibility of conflict among them. We consider the asymptotic Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. These three test statistics have identical limiting chi-square distributions; thus their critical regions coincide. A strong result we obtain is that a systematic numerical inequality relationship exists; specifically, Wald , LRa LM. Since the equality relationship holds only if the null hypothesis is exactly true in the sample, in practice there will always exist a significance level for which the asymptotic Wald, LR, and LM tests will yield conflicting inference. However, when the null hypothesis is true, the dispersion among the teststatistics will tend to decrease as the sample size increases. We illustrate relationships among the alternative testing criteria with an empirical example based on the three reduced form equations of Klein's Model I of the United States economy, 1921-1941.

In this paper, the problem of estimation of the regression coefficients in a multiple regression model with multivariate Student-t error is considered under the multicollinearity situation when it is suspected that the regression coefficients may be restricted to a linear manifold. The preliminary test Liu estimators (PTLE) based on the Wald, Likelihood ratio (LR) and Lagrangian multiplier (LM) tests are given. The bias and mean square error (MSE) of the proposed estimators are derived and conditions of superiority of these estimators are provided. In particular, we show that in the neighborhood of the null hypothesis, the PTLE based on the LM test has the best performance followed by the estimators based on LR and W tests, while the situation is reversed when the parameter moves away from the manifold of the restriction. Furthermore, the optimum choice of the level of significance is also discussed.

The paper considers the problem of testing error serial correlation of partially linear additive measurement error model. We propose a test statistic and show that it converges to the standard chi-square distribution under the null hypothesis. Finally, a simulation study is conducted to illustrate the performance of the test approach.

Expectations Hypotheses Tests

Testing panel data regression models with spatial error correlation

Tests for serial correlation of unknown form in dynamic least squares regression with wavelets

SUMMARY In order to test for serial correlation in residuals for static time series regression in the presence of missing data, the score principle is applied both to the likelihood conditional on the observation times, and to an unconditional form of likelihood. Asymptotic distributions of the test statistics are established, under both the null hypothesis of no serial correlation, and sequences of local, correlated, alternatives, enabling analytic comparison of efficiency.

This paper considers testing the null hypothesis that a times series is uncorrelated when the time series is uncorrelated but statistically dependent. This case is of interest in economic and finance applications. The GARCH(1, 1) model is a leading example of a model that generates serially uncorrelated but statistically dependent data. The tests of serial correlation introduced by Andrews and Ploberger (1996, hereafter AP) are generalized for the purpose of testing the null. The rationale for generalizing the AP tests is that they have attractive properties for cases for which they were originally designed: they are consistent against all nonwhite-noise alternatives and have good all-round power against nonseasonal alternatives compared to several widely used tests in the literature. These properties are inherited by the generalized AP tests.

Multi-scale tests for serial correlation

This paper tests the weak-form of the efficient market hypothesis (EMH) of the Nairobi Securities Exchange (NSE) using daily and weekly index data from the NSE 20 share index over the period, January 2001 to January 2015 and the NSE All Share Index (ASI) from its initiation, in February 2008 to January 2015. To test weak-form efficiency in this market, this study uses the serial correlation test, unit root tests (ADF and Phillips-Perron) and runs test. Results indicate that we cannot accept the EMH for the NSE using the serial correlation test, unit root tests and the runs test. Overall, the Kenyan market is found to not be weak-form efficient