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Fast exact finite-sample back-testing for Value-at-Risk (VaR) models in R.
ExactVaRTest provides fast dynamic-programming algorithms in C++/Rcpp (with pure R fallbacks) for the exact finite-sample distributions and p-values of Christoffersen (1998) independence (IND) and conditional-coverage (CC) VaR backtests. For completeness, it also provides the exact unconditional-coverage (UC) test following Kupiec (1995) via a closed-form binomial enumeration.
In particular, it corrects the severe size distortions from which the usual asymptotic \(\chi^2\) approximation suffers in small samples and under extreme coverage rates.
backtest_lr() returns the LR statistic, its exact
p‑value, and a reject / fail‑to‑reject decision for one chosen test type
(UC, IND, or CC).
backtest_all() runs the UC, IND, and CC tests
jointly and returns summaries for all three statistics.
You can install the development version of ExactVaRTest from GitHub with:
# install.packages("pak")
pak::pak("YujianCHEN219/ExactVaRTest")library(ExactVaRTest)
set.seed(42)
x <- rbinom(300, 1, 0.03) # synthetic 0/1 exception series
bt <- backtest_lr(x, alpha = 0.05, type = "cc") # exact LR_cc back-test
print(bt)
#> Exact finite-sample back-test
#> --------------------------------
#> Test : Conditional coverage (LR_cc)
#> Sample size : 300
#> Model alpha : 0.0500
#> Signif. level : 0.0500
#> LR statistic : 5.8882
#> Exact p-value : 0.0442
#> Decision : REJECT null at 5.00% levelExact finite‑sample distributions and p‑values for LR_ind and LR_cc at any sample size n; for n ≤ 2000 the computation finishes in milliseconds to a few seconds.
C++ implementation via Rcpp, with automatic fallback
to a pure‑R reference engine.
Minimal dependencies (Rcpp, stats);
works on macOS, Linux, and Windows.
Freely extends to CoVaR backtesting: pass the institution’s
hit sequence on system‑VaR‑breach days into backtest_lr()
for exact UC/IND p‑values; for short windows or extreme tails, one
option is to treat the systemic‑breach count as random and apply the
mixture‑tail test to maintain correct size. (see vignettes and [Francq
& Zakoïan 2025]).
Christoffersen, P. F. (1998). Evaluating interval forecasts. International economic review, 841-862.
Mehta, C. R., Patel, N. R., & Gray, R. (1985). Computing an exact confidence interval for the common odds ratio in several 2× 2 contingency tables. Journal of the American Statistical Association, 80(392), 969-973.
Francq, C., & Zakoïan, J. M. (2025). Inference on dynamic systemic risk measures. Journal of Econometrics, 247, 105936.
I greatly appreciate Christian Francq, Christophe Hurlin, and Jean-Michel Zakoïan’s guidance and support.
In particular, Christian Francq generously shared the initial idea; without his help, this package would not exist.
This package is free and open source, licensed under GPL.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.