Robust Tests For Normality Research Articles

Stochastic approach to heterogeneity in short-time announcement effects on the Chilean stock market indexes within 2016-2019

We aim to examine stock market returns before and after key events in the U.S. Sino trades between 2016 and 2019. The study tracks Cumulative Abnormal Returns (CAR) of the Índice de Precio Selectivo de Acciones (IPSA or S&P/CLX IPSA is a Chilean stock market index) for 26 important events throughout this time period. By testing for both directions and significance of market reaction to said events this study aims to clarify if these events and policy announcements were sufficient to influence local equity markets, and in which direction. A simple analysis of CAR showed 16 negative reactions and 10 Positive reactions. An estimated 13 billion USD in market capitalization was lost as a result. Of the 26 events studied 18 were found to produce statistically significant reactions and 8 did not. The IPSA’s reaction to the significant events was mixed with 11 negative reactions and 7 positive reactions. We also checked for the normality of the distribution by robust normality tests and expected returns possess significant asymmetry and above-normal kurtosis. As such on aggregate it can be concluded that Chilean capital markets reacted negatively to the U.S. Sino trade war. We model IPSA in the period 2016–2022, where we can observe qualitative differences before and after 2019. To the best knowledge of the authors, the model of IPSA in this article is the first attempt in this direction.

On improved volatility modelling by fitting skewness in ARCH models

ABSTRACTWe study ARCH/GARCH effects under possible deviation from normality. Since skewness is the principal cause for deviations from normality in many practical applications, e.g. finance, we study in particular skewness. We propose robust tests for normality both for NoVaS and modified NoVaS transformed and original data. Such an approach is not applicable for EGARCH, but applicable for GARCH-GJR models. A novel test procedure is proposed for the skewness in autoregressive conditional volatility models. The power of the tests is investigated with various underlying models. Applications with financial data show the applicability and the capabilities of the proposed testing procedure.

Small sample robust approach to outliers and correlation of atmospheric pollution and health effects in Santiago de Chile

Adverse effects of air pollution on health are a global problem. Chile is no exception due to the increase of urban population and increasing pollution sources. For several years in the winter months in Santiago de Chile, environmental pre-emergency is decreed, which is due to the increase of measurements of contaminants and the risk that this means to health. In order to model the effects of pollution on health we consider a hierarchical Bayesian generalized linear mixed autoregressive model proposed by Ref. [18]. In particular, we apply the model to the number of children with respiratory diseases in the town of Santiago for the period June–August 2011, using the PM2.5 data as covariate obtained by a spatiotemporal pollution model. In order to detect anomalous data, we apply to residuals both robust normality tests together with novel method of probabilities for mild or extreme outliers. We detected significant heterogeneity between stations which offer us better monitoring planning for the future.AMS 2010 subject classifications. Primary 60K10; Secondary 60E15, 60E05, 62F10.

Identifying Outliers in Finance

Outliers represent a fundamental challenge in empirical finance research. We investigate whether the routine techniques used in finance research to identify and treat outliers are appropriate for the data structures we observe in practice. Specifically, we propose a multivariate identification strategy that can effectively detect outliers. We also introduce an estimator that minimizes the bias outliers cause in both cross-sectional and panel regressions and provide outlier mitigation guidance. Using replications of four recently published studies in premier finance journals, we show how adjusting for multivariate outliers can lead to significantly different results. NOTE: Updated (04/22/2021) outlier robust estimator packages available via STATA's SSC. Note that moremata should be updated (to the latest version on SSC) for these packages to work. These packages are: 1) robstat that estimates various classic and robust measures of location, scale, skewness, and kurtosis, and, optionally, performs robust tests for normality. Jann, B., V. Verardi, C. Vermandele (2018). robstat: Stata module to estimate robust univariate statistics. Available from http://ideas.repec.org/c/boc/bocode/s458524.html. 2) robmv that computes several estimators of multivariate location and scatter (MCD, MVE, M, S, MM, and S-D). Post-estimation command predict can be used after robmv to generate variables identifying multivariate outliers, containing robust distances, etc. Jann, B., V. Verardi, C. Vermandele (2021). robmv: Stata module for robust multivariate estimation of location and covariance. Available from http://ideas.repec.org/c/boc/bocode/s458895.html 3) robreg that provides a number of robust estimators for linear regression models (LS, QUANTILE, MVE, LTS, M,S and MM) and has been modified with respect to the previous version. It now allows time-series operators, factor variables, clustered standard errors etc. Jann, B. (2021). robreg: Stata module providing robust regression estimators. Available from http://ideas.repec.org/c/boc/bocode/s458931.html. 4) xtrobreg that provides robust pairwise-differences estimators for panel data. The “convert” subcommand allows to transform the data permanently and when applying robreg manually one gets (using weights) the equivalent of xtrobreg. The advantage of the conversion is that pairwise differences could then be used with any estimator available in Stata. Jann, B., V. Verardi (2021). xtrobreg: Stata module providing pairwise-differences and first-differences robust regression estimators. Available from http://ideas.repec.org/c/boc/bocode/s458937.html. As far as point 4 is concerned, xtrobreg supersedes the xtrobust command developed for this paper. It is conceptually similar but is not identical in particular for unbalanced data, for the way in which it deals with missing values and gaps and the way in which dummy variables are treated.

Geometric aspects of robust testing for normality and sphericity

ABSTRACTStochastic robustness of control systems under random excitation motivates challenging developments in geometric approach to robustness. The assumption of normality is rarely met when analyzing real data and thus the use of classic parametric methods with violated assumptions can result in the inaccurate computation of p-values, effect sizes, and confidence intervals. Therefore, quite naturally, research on robust testing for normality has become a new trend. Robust testing for normality can have counterintuitive behavior, some of the problems have been introduced in Stehlík et al. [Chemometrics and Intelligent Laboratory Systems 130 (2014): 98–108]. Here we concentrate on explanation of small-sample effects of normality testing and its robust properties, and embedding these questions into the more general question of testing for sphericity. We give geometric explanations for the critical tests. It turns out that the tests are robust against changes of the density generating function within the class of all continuous spherical sample distributions.

VYUŽITÍ DISTRIBUČNÍCH A KORELAČNÍCH TESTŮ PRO TESTOVÁNÍ HYPOTÉZY EFEKTIVNOSTI ČESKÉHO KAPITÁLOVÉHO TRHU

This paper deals with efficiency testing of the Czech stock market. In this work there are defined different forms of efficiency, whereas key attention is focused on the weak-form of market efficiency. The goal of this paper is to find the weak-form of efficiency with the help of various tests. We have used some basic methods for our analysis: the autocorrelation coefficient, the Ljung-Box test and selected tests of normality – some classical normality tests (the Shapiro-Wilk test, the Jarque-Bera test, the Lilliefors test) and some robust normality tests (the robust Jarque-Bera test, the directed SJ test and medcouple MC-LR test). Source data for purpose of testing of weak-form of efficiency include years from 2000 to 2008, whereas daily and monthly logarithmic returns of the stock exchange market index PX are analyzed. In this paper we also analyze the daily and monthly logarithmic returns of the U.S. stock exchange market index DJI for purposes of comparison.

ANALÝZA SÍLY VYBRANÝCH KLASICKÝCH A ROBUSTNÍCH TESTŮ NORMALITY PROTI BIMODÁLNÍMU ROZDĚLENÍ

The aim of this paper is to compare the power of selected normality tests to detect a bimodal distribution. We use some classical normality tests (the Shapiro-Wilk test, the Lilliefors test, the Anderson-Darling test, the classical Jarque-Bera test and the Jarque-Bera-Urzua test), some robust normality tests (the robust Jarque-Bera test and the Medcouple test) and the modified Jarque-Bera tests, where the median instead of the mean is used in the classical Jarque-Bera test statistic. The results of simulation study show that the Anderson-Darling and the Shapiro-Wilk tests outperform the others, especially in small sample sizes. On the other hand the classical Jarque-Bera, the Jarque-Bera-Urzua and robust Jarque-Bera tests are biased, especially in small sample sizes again. Finally, the modification of the Jarque-Bera test leads to increase of power against bimodal distribution.

On robust testing for normality in chemometrics

The assumption that the data has been generated by a normal distribution underlies many statistical methods used in chemometrics. While such methods can be quite robust to small deviations from normality, for instance caused by a small number of outliers, common tests for normality are not and will often needlessly reject normality. It is therefore better to use tests from the little-known class of robust tests for normality. We illustrate the need for robust normality testing in chemometrics with several examples, review a class of robustified omnibus Jarque–Bera tests and propose a new class of robustified directed Lin–Mudholkar tests. The robustness and power of several tests for normality are compared in a large simulation study. The new tests are robust and have high power in comparison with both classic tests and other robust tests. A new graphical method for assessing normality is also introduced.

Small Sample Robust Testing for Normality against Pareto Tails

The aim of this article is to introduce the general form (so called RT class) of the robust and classical Jarque–Bera (JB) test based on the location functional. We introduce the two-step procedure which is optimal for testing against the individual or contaminated Pareto alternative. As a reference for such a contamination we consider different Pareto distributions. We also give practical guidelines for robust testing for normality against short- and heavy-tailed alternatives. We concentrate mainly on simulation results for moderate and small samples. However, we also prove consistency and asymptotic distribution for introduced tests. We show that as the suitable measure of nominal level of Pareto tail parameter we may take the t-Hill estimator introduced in the article. To guarantee the consistency of the whole procedure, we also prove the consistency of t-Hill estimator. The introduced general class of robust tests of the normality is illustrated at the selected datasets of financial time series.

Lawstat: AnRPackage for Law, Public Policy and Biostatistics

We present a new R software package lawstat that contains statistical tests and procedures that are utilized in various litigations on securities law, antitrust law, equal employment and discrimination as well as in public policy and biostatistics. Along with the well known tests such as the Bartels test, runs test, tests of homogeneity of several sample proportions, the Brunner-Munzel tests, the Lorenz curve, the Cochran-Mantel-Haenszel test and others, the package contains new distribution-free robust tests for symmetry, robust tests for normality that are more sensitive to heavy-tailed departures, measures of relative variability, Levene-type tests against trends in variances etc. All implemented tests and methods are illustrated by simulations and real-life examples from legal cases, economics and biostatistics. Although the package is called lawstat, it presents implementation and discussion of statistical procedures and tests that are also employed in a variety of other applications, e.g., biostatistics, environmental studies, social sciences and others, in other words, all applications utilizing statistical data analysis. Hence, name of the package should not be considered as a restriction to legal statistics. The package will be useful to applied statisticians and

Robust tests for normality of errors in regression models

This paper investigates the effects of using residuals from robust regression in place of OLS residuals in test statistics for the normality of the errors. It is found that for systematic and clustered outliers, robustified normality tests yield greater power.