% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/svp_test.R
\name{mmc_ar}
\alias{mmc_ar}
\title{MMC Test for AR Order in SV(p) Models}
\usage{
mmc_ar(
  y,
  p_null,
  p_alt,
  J = 10,
  N = 99,
  burnin = 500,
  eps = NULL,
  threshold = 1,
  method = "pso",
  maxit = NULL,
  del = 1e-10,
  wDecay = FALSE,
  Bartlett = FALSE,
  Amat = NULL,
  errorType = "Gaussian",
  sigvMethod = "factored",
  logNu = TRUE,
  winsorize_eps = 0
)
}
\arguments{
\item{y}{Numeric vector. Observed returns.}

\item{p_null}{Integer. Order under the null hypothesis.}

\item{p_alt}{Integer. Order under the alternative (\code{p_alt > p_null}).}

\item{J}{Integer. Winsorizing parameter. Default 10.}

\item{N}{Integer. Number of Monte Carlo replications. Default 99.}

\item{burnin}{Integer. Burn-in for simulation. Default 500.}

\item{eps}{Numeric vector. Half-width of search region around estimated
nuisance parameters. Default \code{rep(0.3, p_null+2)}.}

\item{threshold}{Numeric. Target p-value. Default 1.}

\item{method}{Character. Optimization method: \code{"pso"} or \code{"GenSA"}.
Default \code{"pso"}.}

\item{maxit}{Integer. Maximum iterations/evaluations. Default depends on method.}

\item{del}{Numeric. Small constant for log transformation. Default \code{1e-10}.}

\item{wDecay}{Logical. Use decaying weights. Default \code{FALSE}.}

\item{Bartlett}{Logical. If \code{TRUE}, use Bartlett kernel HAC weighting
matrix for a GMM-LRT-type test statistic. If \code{FALSE} (default), use
the sum of squared extra AR coefficients.}

\item{Amat}{Weighting matrix specification. \code{NULL} (default) for identity
weighting, or \code{"Weighted"} for data-driven HAC. Takes precedence over
\code{Bartlett}. User-supplied matrices are not supported for AR order tests.}

\item{errorType}{Character. Error distribution of the return innovations:
\code{"Gaussian"} (default), \code{"Student-t"}, or \code{"GED"}. Heavy-tail
options reuse the same moment-based GMM-LRT machinery as \code{lmc_t}/
\code{lmc_ged}; \eqn{\nu} is held at the null MLE during the simulation
(it is not a varied nuisance for the AR-order test).}

\item{sigvMethod}{Character. Method for \eqn{\sigma_v} estimation:
\code{"factored"} (default), \code{"hybrid"}, or \code{"direct"}.}

\item{logNu}{Logical. Use log-space for \eqn{\nu} estimation (Student-t/GED
only). Default \code{TRUE}.}

\item{winsorize_eps}{Number of extreme autocovariance lags to winsorize
(heavy-tail only). Default 0.}
}
\value{
A list with optimization output including \code{value} (maximized p-value)
  and \code{par} (nuisance parameters at the maximum).
}
\description{
Performs a Maximized Monte Carlo (MMC) test of
\eqn{H_0: \phi_{p_0+1} = \cdots = \phi_p = 0}
by maximizing the MC p-value over nuisance parameters
(\eqn{\phi_1, \ldots, \phi_{p_0}, \sigma_y, \sigma_v}).
}
\examples{
\donttest{
y <- sim_svp(1000, phi = 0.95, sigy = 1, sigv = 0.2)$y
mmc <- mmc_ar(y, p_null = 1, p_alt = 2, J = 10, N = 19,
              method = "pso", maxit = 10)
mmc$value
}

}
