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1

Testing for a serial correlation in VaR failures through the exponential autoregressive conditional duration model

100%

Małecka M.

Statistics in Transition new series

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2021

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vol. 22

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issue 1

145-162

EN

Although regulatory standards, currently developed by the Basel Committee on Banking Supervision, anticipate a shift from VaR to ES, the evaluation of risk models currently remains based on the VaR measure. Motivated by the Basel regulations, we address the issue of VaR backtesting and contribute to the debate by exploring statistical properties of the exponential autoregressive conditional duration (EACD) VaR test. We show that, under the null, the tested parameter lies at the boundary of the parameter space, which can profoundly affect the accuracy of this test. To compensate for this deficiency, a mixture of chi-square distributions is applied. The resulting accuracy improvement allows for the omission of the Monte Carlo simulations used to implement the EACD VaR test in earlier studies, which dramatically improves the computational efficiency of the procedure. We demonstrate that the EACD approach to testing VaR has the potential to enhance statistical inference in most problematic cases - for small samples and for those close to the null.

2

On permutation location–scale tests

100%

Polko-Zając D.

Statistics in Transition new series

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2019

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vol. 20

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issue 4

153-166

EN

Statisticians are constantly looking for methods of statistical inference that would be both effective and would require meeting as few assumptions as possible. Permutation tests seem to fit here, as using them makes it possible to perform statistical inference in situations where classical parametric tests do not work. Permutation tests appear to be comparably powerful to parametric tests, but require meeting fewer assumptions, e.g. regarding the size of the sample or the from of distribution of the tested variable in a population. The presented tests make it possible to verify the overall hypothesis about the identity of both location and scale parameters in the studied populations. In literature, the Lepage test and the Cucconi test are most often referred to in this context. The paper considers various forms of test statistics, and presents a simulation study carried out to determine the size and power of the tests under normality. As the study demonstrated, the advantage of the proposed method is that it can be applied to small-size samples. A nonparametric, complex procedure was used to assess the overall ASL (achieved significance level) value by applying the permutation principle. For comparative purposes, the results for the permutation Lepage test and the permutation Cucconi test are also presented.

3

Badania symulacyjne związane z wyznaczaniem liczebności próby w teście Manna‑Whitneya w przypadku rozkładu Pareto

51%

Kornacki A., Bochniak A.

Acta Universitatis Lodziensis. Folia Oeconomica

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2019

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vol. 1

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issue 340

27-42

EN

In the paper, the problem of determination of the number of observations necessary for the appropriate use of the non‑parametric Mann‑Whitney test in the case of Pareto distribution is presented. Using the method provided by Noether, the sample size is calculated which guarantees that the Mann‑Whitney U test at a given significance level α has the pre‑assumed power 1 –β. The presented method is examined by calculating empirical power in computer simulations. Moreover, different techniques of rounding the estimated sample size to an even integer number are studied. It is important when two equinumerous samples are to be compared.

PL

W artykule poruszony został problem wyznaczenia liczby obserwacji niezbędnej do poprawnego stosowania nieparametrycznego testu Manna‑Whitneya. W rozważaniach rozpatrywane są próby pochodzące z populacji o rozkładzie Pareto. Korzystając z metody podanej przez G. E. Noethera, szacowany jest rozmiar próby, który gwarantuje, że test Manna‑Whitneya ma z góry ustaloną moc 1 – β na danym poziomie istotności α. W pracy teoretyczna moc testu jest porównywana z mocą empiryczną oszacowaną przez symulacje komputerowe. Ponadto badany jest wpływ różnych metod zaokrąglania estymowanej wielkości próby do liczby parzystej, gdy porównywane są dwie równoliczne próby.

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2 Statistics in Transition new series

1 Acta Universitatis Lodziensis. Folia Oeconomica

1 Bochniak A.

1 Kornacki A.

1 Małecka M.

1 Polko-Zając D.

1 2021

2 2019

Testing for a serial correlation in VaR failures through the exponential autoregressive conditional duration model

On permutation location–scale tests

Badania symulacyjne związane z wyznaczaniem liczebności próby w teście Manna‑Whitneya w przypadku rozkładu Pareto