Title: Exact Finite-Sample Value-at-Risk Back-Testing
Version: 0.1.3
Language: en-US
Maintainer: Yujian Chen <yjc4996@gmail.com>
Description: 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. See Christoffersen (1998) <doi:10.2307/2527341> and Kupiec (1995) <doi:10.3905/jod.1995.407942>.
License: GPL (≥ 3)
Depends: R (≥ 3.5.0)
Imports: Rcpp, stats
LinkingTo: Rcpp
Suggests: bench, dplyr, tidyr, purrr, ggplot2, xts, quantmod, knitr, rmarkdown, testthat (≥ 3.0.0)
Encoding: UTF-8
RoxygenNote: 7.3.2
URL: https://github.com/YujianCHEN219/ExactVaRTest
BugReports: https://github.com/YujianCHEN219/ExactVaRTest/issues
Acknowledgements: I greatly appreciate Christian Francq, Christophe Hurlin, and Jean-Michel Zakoian's guidance and support. In particular, Christian Francq generously shared the initial idea; without his help, this package would not exist.
Config/testthat/edition: 3
VignetteBuilder: knitr
NeedsCompilation: yes
Packaged: 2025-08-18 19:43:47 UTC; chenyujian
Author: Yujian Chen [aut, cre]
Repository: CRAN
Date/Publication: 2025-08-22 17:20:02 UTC

ExactVaRTest – Exact Finite-Sample VaR Back-Testing

Description

Provides fast dynamic‑programming algorithms (C++/Rcpp) – with pure‑R fall‑backs – for the exact finite‑sample distributions and p‑values of Christoffersen’s (1998) VaR back‑tests: Independence (IND) and Conditional Coverage (CC) tests, and the Unconditional Coverage (UC) test via closed‑form binomial enumeration.

Author(s)

Maintainer: Yujian Chen yjc4996@gmail.com

See Also

Useful links:

Exact UC/IND/CC back‑tests in one call

Description

Exact UC/IND/CC back‑tests in one call

Usage

backtest_all(x, alpha = 0.05, sig = 0.05, prune_threshold = 1e-15)

Arguments

x

0/1 exception series.

alpha

Exception probability.

sig

Significance level (default 0.05).

prune_threshold

Passed to the dynamic programming engine.

Value

An object of class "ExactVaRBacktestAll" (a named list) with components: uc, ind, cc (each a list with stat, pval, reject), and scalars sig (significance level), alpha (model exception probability), n (sample size).

Examples

set.seed(1)
x <- rbinom(300, 1, 0.02)
backtest_all(x, alpha = 0.02)

Exact finite‑sample back‑test for a VaR exception series

Description

Exact finite‑sample back‑test for a VaR exception series

Usage

backtest_lr(
  x,
  alpha = 0.05,
  type = c("uc", "ind", "cc"),
  sig = 0.05,
  prune_threshold = 1e-15
)

Arguments

x

0/1 exception series.

alpha

Exception probability.

type

"uc", "ind" or "cc".

sig

Significance level (default 0.05).

prune_threshold

Passed to the dynamic‑programming engine.

Value

An object of class "ExactVaRBacktest" (a named list) with components: stat (numeric LR statistic), pval (numeric exact p-value in [0,1]), reject (logical; TRUE if p < sig), type (character; one of "uc", "ind", "cc"), alpha (numeric model exception probability), sig (numeric significance level), n (integer sample size).

Examples

set.seed(123)
x <- rbinom(250, 1, 0.01)
backtest_lr(x, alpha = 0.01, type = "uc")

Exact LR_cc (and LR_uc) distribution (auto‑select engine)

Description

Returns the finite‑sample distribution of Christoffersen’s conditional‑coverage statistic LR_{\mathrm{cc}}. The returned list also includes the matching unconditional‑coverage distribution LR_{\mathrm{uc}}, produced by the same dynamic‑programming run.

Usage

lr_cc_dist(n, alpha = 0.05, prune_threshold = 1e-15)

Arguments

n

Integer sample size (n \ge 1).

alpha

Exception probability \alpha \in (0,1).

prune_threshold

Probability below which states are pruned by the dynamic‑programming recursion.

Value

A named list with elements LR_cc, prob_cc, LR_uc, prob_uc. The pairs (LR_cc, prob_cc) and (LR_uc, prob_uc) have equal lengths; each probability vector is in [0,1] and sums to 1.

Examples

lr_cc_dist(8, 0.05)

Christoffersen LR_cc statistic

Description

Christoffersen LR_cc statistic

Usage

lr_cc_stat(x, alpha = 0.05)

Arguments

x

0/1 exception series.

alpha

Exception probability.

Value

Numeric LR_cc statistic.

Exact LR_ind distribution (auto‑select engine)

Description

Returns the finite‑sample distribution of Christoffersen’s independence statistic LR_{\mathrm{ind}}.

Usage

lr_ind_dist(n, alpha = 0.05, prune_threshold = 1e-15)

Arguments

n

Integer sample size (n \ge 1).

alpha

Exception probability \alpha \in (0,1).

prune_threshold

Probability below which states are pruned by the dynamic‑programming recursion.

Value

A named list with elements LR and prob of equal length, where LR is the support of the LR statistic and prob are the corresponding probabilities in [0,1] that sum to 1.

Examples

lr_ind_dist(8, 0.05)

Christoffersen LR_ind statistic

Description

Christoffersen LR_ind statistic

Usage

lr_ind_stat(x, alpha = 0.05)

Arguments

x

0/1 exception series.

alpha

Exception probability.

Value

Numeric LR_ind statistic.

Exact LR_uc distribution (closed‑form binomial)

Description

Exact LR_uc distribution (closed‑form binomial)

Usage

lr_uc_dist(n, alpha = 0.05)

Arguments

n

Integer sample size (n \ge 1).

alpha

Exception probability \alpha \in (0,1).

Value

A named list with elements LR and prob of equal length, where LR is the support of the LR statistic and prob are the corresponding probabilities in [0,1] that sum to 1.

Examples

lr_uc_dist(8, 0.01)

Christoffersen LR_uc statistic

Description

Christoffersen LR_uc statistic

Usage

lr_uc_stat(x, alpha = 0.05)

Arguments

x

0/1 exception series.

alpha

Exception probability.

Value

Numeric LR_uc statistic.

Print method for ExactVaRBacktest

Description

Print method for ExactVaRBacktest

Usage

## S3 method for class 'ExactVaRBacktest'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

An object of class 'ExactVaRBacktest'.

digits

Number of digits to print.

...

Further arguments passed to or from other methods (ignored).

Details

Prints the test name, sample size n, model alpha, significance level, LR statistic, exact p-value, and the decision at the specified level.

Value

The input object x, returned invisibly (class ExactVaRBacktest).

Print method for ExactVaRBacktestAll

Description

Print method for ExactVaRBacktestAll

Usage

## S3 method for class 'ExactVaRBacktestAll'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x

An object of class 'ExactVaRBacktestAll'.

digits

Number of digits to print.

...

Further arguments passed to or from other methods (ignored).

Details

Prints a header with sample size n, model alpha and significance level, followed by per-test blocks for UC, IND, and CC: LR statistic, exact p-value, and the decision at the specified level.

Value

The input object x, returned invisibly (class ExactVaRBacktestAll).

Exact p-value for LR_cc

Description

Exact p-value for LR_cc

Usage

pval_lr_cc(lr_obs, n, alpha = 0.05, prune_threshold = 1e-15)

Arguments

lr_obs

Observed LR_cc statistic.

n

Sample size.

alpha

Exception probability.

prune_threshold

State-pruning threshold for DP engine.

Value

Numeric exact p-value in [0,1]; may be NA_real_ if the finite-sample distribution is unavailable.

Exact p-value for LR_ind

Description

Exact p-value for LR_ind

Usage

pval_lr_ind(lr_obs, n, alpha = 0.05, prune_threshold = 1e-15)

Arguments

lr_obs

Observed LR_ind statistic.

n

Sample size.

alpha

Exception probability.

prune_threshold

State-pruning threshold for DP engine.

Value

Numeric exact p-value in [0,1]; may be NA_real_ if the finite-sample distribution is unavailable.

Exact p-value for LR_uc

Description

Exact p-value for LR_uc

Usage

pval_lr_uc(lr_obs, n, alpha = 0.05)

Arguments

lr_obs

Observed LR_uc statistic.

n

Sample size.

alpha

Exception probability.

Value

Numeric exact p-value in [0,1]; may be NA_real_ if the finite-sample distribution is unavailable.