A simple and focused backtest of value at risk

Abstract

We suggest a simple improvement of recent VaR-backtesting procedures based on time intervals between VaR-exceedances and show via Monte Carlo that our test has more power than its competitors against empirically relevant clustering alternatives.

Estimation risk taking into consideration the effect of forecasting scheme: robust inference about VaR

“…A large group of the methods proposed as the follow-up to the pioneering tests mentioned before can be classified as duration-based tests. They use the transformation of VaR violations into durations and include tests proposed by Berkowitz et al (2011), Candelon et al (2011, Christoffersen and Pelletier (2004), Engle and Russel (1998), Haas (2005), Krämer and Wied (2015), Pelletier and Wei (2016) and Ziggel et al (2014).…”

“…To represent the class of the duration-based VaR tests, we selected the geometric-VaR test by Pelletier and Wei (2016). This method generalises the geometric approach proposed by Christoffersen and Pelletier (2004) and follows a number of other VaR testing procedures related to the geometric distribution (Berkowitz et al, 2011;Candelon et al, 2011;Engle & Russel, 1998;Haas, 2005;Krämer & Wied, 2015;Ziggel et al, 2014). The spectral methods, following research by Małecka (2016), are represented in our study by the Anderson-Darling VaR test, which draws upon the spectral approach proposed by Berkowitz et al (2011).…”

New runs‐based approach to testing value at risk forecasts

“…1 A separate intensely developed line of research is built on the transformation of the VaR failure series into the duration series, which assures power against dependencies of a general form. The durationbased framework relies on the properties of the memoryfree geometric and exponential distributions (Berkowitz et al, 2011;Candelon et al, 2011;Christoffersen & Pelletier, 2004;Haas, 2006;Kramer & Wied, 2015;Malecka, 2022;Pelletier & Wei, 2016;Ziggel et al, 2014).…”

A review of backtesting for value at risk

“…This paper provides a comprehensive review of backtesting methods for VaR. The methods reviewed include: the simplest backtesting method, binomial distribution test, Kupiec's POF (1995) test, Kupiec's TUFF test, proportion of failures test (Haas, 2001), time between failures likelihood ratio test (Haas, 2001), scaled Crnkovic and Drachman (1996)'s method (Haas, 2001), density forecast tests (Berkowitz, 2000(Berkowitz, , 2001), Lopez's magnitude loss function (Lopez, 1998(Lopez, , 1999, risk map (Colletaz et al, 2013), independence test (Christoffersen, 1998), joint test, generalized Markov tests (Pajhede, 2015), the Basel Committee's traffic light test, quality control of risk measure (de la Pena et al, 2006), duration -based tests (Christoffersen andPelletier, 2004, Berkowitz et al, 2011), Haas (2006)'s test, generalized method of moments duration -based test (Hurlin et al, 2010), conditional duration test (Christoffersen and Pelletier, 2002), Krämer and Wied (2015)'s test, Markov duration tests (Pajhede, 2015), Olmo (2010, 2011)'s tests, Wald statistic test (Engle and Managanelli, 2004), dynamic binary tests (Dumitrescu et al, 2012), multivariate test (Perignon and Smith, 2008), martingale difference test (Berkovitz et al, 2005), multivariate autocorrelations test (Hurlin and Tokpavi, 2006), geometric-VaR backtesting method (Pelletier and Wei, 2015).…”