Package 'ExactVaRTest'

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 [email protected]

See Also

Useful links:

• https://github.com/YujianCHEN219/ExactVaRTest

• Report bugs at https://github.com/YujianCHEN219/ExactVaRTest/issues

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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)

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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.

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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.

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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).

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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.

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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.

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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.

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