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

Marta Małecka

doi:10.21307/stattrans-2021-008

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

Marta Małecka Department of Statistical Methods, University of Łódź, Poland ORCID:http://orchid.org/0000-0003-4465-9811 Statistics in Transition new series, vol. 22, 2021, 1, pages: 145–162 Published online: 3 March 2021 DOI 10.21307/stattrans-2021-008

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ABSTRACT

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.

KEYWORDS

VaR backtesting, exponential autoregressive conditional duration, boundary of the parameter space, test size, test power

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