Econometrics 2015, 3(3), 532-560; https://doi.org/10.3390/econometrics3030532
New Graphical Methods and Test Statistics for Testing Composite Normality
1
Department of Banking and Finance, University of Zurich, Plattenstrasse 14, 8032 Zurich, Switzerland
2
Swiss Finance Institute, Walchestrasse 9 CH-8006 Zurich, SwitzerlandÂ
Academic Editor: Kerry Patterson
Received: 28 January 2015 / Revised: 29 June 2015 / Accepted: 29 June 2015 / Published: 15 July 2015
Abstract
Several graphical methods for testing univariate composite normality from an i.i.d. sample are presented. They are endowed with correct simultaneous error bounds and yield size-correct tests. As all are based on the empirical CDF, they are also consistent for all alternatives. For one test, called the modified stabilized probability test, or MSP, a highly simplified computational method is derived, which delivers the test statistic and also a highly accurate p-value approximation, essentially instantaneously. The MSP test is demonstrated to have higher power against asymmetric alternatives than the well-known and powerful Jarque-Bera test. A further size-correct test, based on combining two test statistics, is shown to have yet higher power. The methodology employed is fully general and can be applied to any i.i.d. univariate continuous distribution setting. View Full-TextKeywords:
calibration for simultaneity; combined tests; distribution testing; P-P plot; Q-Q plot; simultaneous null bands
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Figure 1a
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Paolella, M.S. New Graphical Methods and Test Statistics for Testing Composite Normality. Econometrics 2015, 3, 532-560.
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