lmc_ar: LMC Test for AR Order in SV(p) Models

In wARMASVp: Winsorized ARMA Estimation for Higher-Order Stochastic Volatility Models

LMC Test for AR Order in SV(p) Models

Description

Performs a Local Monte Carlo (LMC) test of the null hypothesis H_0: \phi_{p_0+1} = \cdots = \phi_p = 0 (i.e., that an SV(p_0) model is sufficient against an SV(p) alternative).

Usage

lmc_ar(
  y,
  p_null,
  p_alt,
  J = 10,
  N = 99,
  burnin = 500,
  del = 1e-10,
  wDecay = FALSE,
  Bartlett = FALSE,
  Amat = NULL,
  errorType = "Gaussian",
  sigvMethod = "factored",
  logNu = TRUE,
  winsorize_eps = 0
)

Arguments

y	Numeric vector. Observed returns.
p_null	Integer. Order under the null hypothesis.
p_alt	Integer. Order under the alternative (p_alt > p_null).
J	Integer. Winsorizing parameter. Default 10.
N	Integer. Number of Monte Carlo replications. Default 99.
burnin	Integer. Burn-in for simulation. Default 500.
del	Numeric. Small constant for log transformation. Default 1e-10.
wDecay	Logical. Use decaying weights. Default FALSE.
Bartlett	Logical. If TRUE, use Bartlett kernel HAC weighting matrix for a GMM-LRT-type test statistic. If FALSE (default), use the sum of squared extra AR coefficients.
Amat	Weighting matrix specification. NULL (default) for identity weighting, or "Weighted" for data-driven HAC. Takes precedence over Bartlett. User-supplied matrices are not supported for AR order tests.
errorType	Character. Error distribution of the return innovations: "Gaussian" (default), "Student-t", or "GED". Heavy-tail options reuse the same moment-based GMM-LRT machinery as lmc_t/ lmc_ged; \nu is held at the null MLE during the simulation (it is not a varied nuisance for the AR-order test).
sigvMethod	Character. Method for \sigma_v estimation: "factored" (default), "hybrid", or "direct".
logNu	Logical. Use log-space for \nu estimation (Student-t/GED only). Default TRUE.
winsorize_eps	Number of extreme autocovariance lags to winsorize (heavy-tail only). Default 0.

Details

When Bartlett = FALSE (default), the test statistic is T \sum_{j=p_0+1}^{p} \hat\phi_j^2, i.e., the sum of squared extra AR coefficients scaled by sample size.

When Bartlett = TRUE, the test statistic is based on the GMM-LRT approach with a Bartlett kernel HAC weighting matrix: S = T \times (M_{H_0} - M_{H_1}), where M denotes the GMM criterion evaluated at the null and alternative estimates. Both the observed and simulated test statistics are capped at 1e-10 when negative; a negative observed statistic raises a warning (it indicates strong evidence in favour of the null, since the alternative does not improve the GMM criterion).

Value

An object of class "svp_test", a list containing:

s0

Test statistic from observed data (capped at 1e-10 if negative).

sN

Simulated null distribution (vector of length N).

pval

Monte Carlo p-value.

test_type

Character string identifying the test.

null_param

Name of the parameter(s) tested.

null_value

Value(s) under the null hypothesis.

errorType

Error distribution used.

call

The matched call.

Examples

y <- sim_svp(1000, phi = 0.95, sigy = 1, sigv = 0.2)$y
test <- lmc_ar(y, p_null = 1, p_alt = 2, J = 10, N = 49)
print(test)

wARMASVp documentation built on May 15, 2026, 5:07 p.m.