Comparison of the Goodness-of-Fit Tests for Truncated Distributions

Agnieszka Lach; Łukasz Smaga

doi:10.5604/01.3001.0014.0541

Agnieszka Lach Poznan University of Economics and Business, Faculty of Informatics and Electronic Economy, Operations Research Department , Łukasz Smaga Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Department of Probability and Mathematical Statistics Przegląd Statystyczny. Statistical Review, vol. 65, 2018, 3, pages: 296-313 Published online: 30 January 2019 DOI 10.5604/01.3001.0014.0541

1008 Views 43 Downloads

ARTICLE

(English) PDF

ABSTRACT

The aim of this paper is to investigate the finite sample behavior of seven goodness-of-fit tests for left truncated distributions of Chernobai et al. (2015) in terms of size and power. Simulation experiments are based on artificial data generated from the distributions that were used in the past or are used nowadays to describe the tails of asset returns. The study was conducted for different tail thickness and for changing truncation point. Simulation results indicate that the testing procedures do not work equally well under finite samples, and some of them require quite large number of observations to perform satisfactorily.

KEYWORDS

goodness of fit tests, power of test, R program, size of test, truncated distributions

REFERENCES

Anderson T. W., Darling D. A., (1952), Asymptotic Theory of Certain ”Goodness of Fit” Criteria Based on Stochastic Processes, The Annals of Mathematical Statistics, 23 (2), 193–212.

Brunner M. I., Viviroli D., Sikorska A. E., Vannier O., Favre A.-C., Seibert J., (2017), Flood Type Specific Construction of Synthetic Design Hydrographs, Water Resources Research, 53 (2), 1390–1406.

Burnecki K., Chechkin A., Wylomanska A., (2015), Discriminating Between Light- and Heavy-Tailed Distributions with Limit Theorem, PLoS ONE, 10 (12), 1–23.

Chernobai A., Burnecki K., Rachev S., Trück S., Weron R., (2006), Modelling Catastrophe Claims with Left-Truncated Severity Distributions, Computational Statistics, 21 (3), 537–555.

Chernobai A., Menn C., Rachev S. T., Trück S., (2010), Estimation of Operational Value-at-Risk in the Presence of Minimum Collection Threshold: An Empirical Study, Working Paper Series in Economics, 4, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.

Chernobai A., Rachev S. T., Fabozzi F. J., (2015), Composite Goodness-of-Fit Tests for Left- Truncated Loss Samples, in: Lee C. F., Lee J., (eds.), Handbook of Financial Econometrics and Statistics, Springer, New York, NY.

Clementi F., Gallegati M., Kaniadakis G., (2012), A New Model of Income Distribution: The ? – Generalized Distribution, Journal of Economics, 105 (1), 63–91.

Cox D. R., Spjotvoll E., Johansen S., Van Zwet W. R., Bithell J. F., Barndorff-Nielsen O., (1977), The Role of Significance Tests, Scandinavian Journal of Statistics, 4 (2), 49–70.

Echaust K., (2014), Ryzyko zdarzeń ekstremalnych na rynku kontraktów futures w Polsce, Wydawnictwo Uniwersytetu Ekonomicznego w Poznaniu, Poznań.

Fagiolo G., Alessi L., Barigozzi M., Capasso M., (2010), On the Distributional Properties of Household Consumption Expenditures: The Case of Italy, Empirical Economics, 38 (3), 717–741.

Feller W., (1950), An Introduction to Probability Theory and Its Applications, Wiley, New York. Fischer M., Jakob K., (2016), pTAS Distributions with Application to Risk Management, Journal of Statistical Distributions and Applications, 3 (1), 1–18.

Górecki T., (2011), Podstawy statystyki z przykładami w R, Wydawnictwo BTC, Legionowo. Górecki T., Smaga Ł., (2015), A Comparison of Tests for the One-Way ANOVA Problem for Functional Data, Computational Statistics, 30, 987–1010.

Guegan D., Hassani B.K., (2018), More Accurate Measurement for Enhanced Controls: VaR vs ES?, Journal of International Financial Markets, Institutions & Money, 54, 152-165.

Haas M., Pigorsch C., (2009), Financial Economics, Fat-Tailed Distributions, Encyclopedia of Complexity and Systems Science, 4, 3404–3435.

Kim J. H., Ji P. I., (2015), Significance Testing in Empirical Finance: A Critical Review and Assessment, Journal of Empirical Finance, 34, 1–14.

Krzyśko M., (2000), Wykłady z teorii prawdopodobieństwa, Wydawnictwa Naukowo-Techniczne, Warszawa.

Krzyśko M., (2004), Statystyka matematyczna, Wydawnictwo Naukowe UAM, Poznań.

Lach A., (2017), Testy zgodności z rozkładami uciętymi, Praca licencjacka, Uniwersytet im. Adama Mickiewicza, Poznań.

Magiera R., (2005), Modele i metody statystyki matematycznej. Cz. 1: Rozkłady i symulacja stochastyczna, Oficyna Wydawnicza GiS, Wrocław.

Mandelbrot B., (1963), The Variation of Certain Speculative Prices, The Journal of Business, 36, 394-419.

Mineo A.M., (2014), normalp: Routines for Exponential Power Distribution, R package version 0.7.0, https://CRAN.R-project.org/package=normalp.

Orzeszko W., (2014), Symulacyjna ocena rozmiaru testu BDS, Przegląd Statystyczny, 4 (61), 335– –361.

Pavia J. M., (2015), Testing Goodness-of-Fit with the Kernel Density Estimator: GoFKernel, Journal of Statistical Software, 66, 1–27.

Piasecki K., Tomasik E., (2013), Rozkłady stóp zwrotu z instrumentów polskiego rynku kapitałowego, Wydawnictwo edu-Libri, Kraków, Warszawa.

R Core Team, (2017), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, http://www.R-project.org/.

Revolution Analytics, Weston S., (2015), doParallel: Foreach Parallel Adaptor for the ’parallel’ Package, R package version 1.0.10, http://CRAN.R-project.org/package=doParallel.

Smaga Ł., (2017), A Two-Sample Test Based on Cluster Subspaces for Equality of Mean Vectors in High Dimension, Discussiones Mathematicae Probability and Statistics, 37, 147–156.

Wolter T., (2012). Truncgof: GoF Tests Allowing for Left Truncated Data, R package version 0.6-0, https://CRAN.R-project.org/package=truncgof.