Testing Hypotheses on the Innovations Distribution in Semi-Parametric Conditional Volatility Models*

Christian Francq and Jean-Michel Zakoian

Journal of Financial Econometrics, 2023, vol. 21, issue 5, 1443-1482

Abstract: Testing symmetry or quantile assumptions on the innovations distribution can be of invaluable help to improve or simplify the statistical procedures designed for GARCH-type models. In particular, evaluation of the conditional value-at-risk (VaR) or construction of confidence intervals for predictions requires estimating quantiles of the innovations distribution. We propose tests of different hypotheses: adequacy of a set of parametric quantiles, mean–median equality, symmetry of extreme quantiles, and zero-median in presence of a conditional mean. The tests rely on the asymptotic distribution of the empirical distribution function of the residuals. They are generally model-free (though not estimation-free) and thus are simple to implement. Efficiency comparisons are made using the Bahadur approach. Numerical studies based on simulated and real data are provided to illustrate the usefulness of the proposed tests for risk management or statistical purposes.

Keywords: asymmetries in financial returns; GARCH innovations; mean–median equality test; quantile testing; testing symmetry of quantiles; value-at-risk (search for similar items in EconPapers)
JEL-codes: C12 C22 C58 (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1093/jjfinec/nbac011 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:jfinec:v:21:y:2023:i:5:p:1443-1482.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Journal of Financial Econometrics is currently edited by Allan Timmermann and Fabio Trojani

More articles in Journal of Financial Econometrics from Oxford University Press Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK. Contact information at EDIRC.
Bibliographic data for series maintained by Oxford University Press ().