% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/optimized_direct_pmm2.R
\name{optimized_direct_pmm2}
\alias{optimized_direct_pmm2}
\title{Optimized Direct Nonlinear PMM2 (DEPRECATED)}
\usage{
optimized_direct_pmm2(
  theta_init,
  y,
  order = c(0, 0, 0),
  seasonal = list(order = c(0, 0, 0), period = NA)
)
}
\arguments{
\item{theta_init}{Initial parameters}

\item{y}{Time series}

\item{order}{ARIMA order}

\item{seasonal}{Seasonal order}
}
\value{
This function will throw an error directing users to unified methods

Optimization result
}
\description{
\strong{DEPRECATED:} This function has been deprecated and should not be used.

\strong{Reason for Deprecation:}
Monte Carlo experiments (R=50, n=200) showed this direct optimization approach
performs catastrophically worse than classical methods:
\itemize{
\item AR(1): 17.0x worse MSE than MLE (3.67 vs 0.22)
\item MA(1): Failed to converge in most replications
\item SARIMA: Severe numerical instability
}

\strong{Recommended Alternatives:}
Use the Unified PMM2 framework instead, which showed 3-23\\% MSE improvements:
\itemize{
\item \code{\link{ar_pmm2}} with \code{pmm2_variant = "unified_global"} (default)
\item \code{\link{arima_pmm2}} with \code{pmm2_variant = "unified_iterative"}
\item \code{\link{ma_pmm2}} with \code{pmm2_variant = "linearized"}
}
}
\details{
This function attempted to directly maximize the PMM2 objective function:
\deqn{J(\theta) = \gamma_3^2 / (2 + \gamma_4)}

However, this objective surface is highly non-convex with many local optima
and flat regions, making direct optimization unreliable. The Unified PMM2
approach (global/iterative corrections from classical estimates) proved far
more stable and accurate.

\strong{Technical Issues:}
\itemize{
\item Objective function has flat regions near optimal values
\item Gradient becomes numerically unstable when \eqn{\gamma_4 \approx -2}
\item Sensitive to initialization (even from MLE estimates)
\item No guarantee of convergence to global optimum
}
}
\references{
Monte Carlo comparison results documented in NEWS.md (Version 0.2.0)
}
\seealso{
\code{\link{ar_pmm2}}, \code{\link{ma_pmm2}}, \code{\link{arima_pmm2}}

Optimized Direct Nonlinear PMM2

Uses analytical gradients to maximize the PMM2 objective function.
J(theta) = gamma3^2 / (2 + gamma4)
}
\keyword{internal}
