\name{dm.test}
\alias{dm.test}
\title{Diebold-Mariano test for predictive accuracy}
\description{The Diebold-Mariano test
compares the forecast accuracy of two forecast methods.}

\usage{
dm.test(e1, e2, alternative=c("two.sided","less","greater"),
    h=1, power=2)
}
\arguments{
  \item{e1}{Forecast errors from method 1.}
  \item{e2}{Forecast errors from method 2.}
  \item{alternative}{a character string specifying the alternative hypothesis, must be one of \code{"two.sided"} (default), \code{"greater"} or \code{"less"}.  You can specify just the initial letter.}
  \item{h}{The forecast horizon used in calculating \code{e1} and \code{e2}.}
  \item{power}{The power used in the loss function. Usually 1 or 2.}
}

\value{
A list with class \code{"htest"} containing the following components:
\item{statistic}{the value of the DM-statistic.}
\item{parameter}{the forecast horizon and loss function power used in the test.}
\item{alternative}{a character string describing the alternative hypothesis.}
\item{p.value}{the p-value for the test.}
\item{method}{a character string with the value "Diebold-Mariano Test".}
\item{data.name}{a character vector giving the names of the two error series.}
}

\details{The null hypothesis is that the two methods have the same forecast accuracy. For \code{alternative="less"}, the alternative hypothesis is that method 2 is less accurate than method 1. For \code{alternative="greater"}, the alternative hypothesis is that method 2 is more accurate than method 1. For \code{alternative="two.sided"}, the alternative hypothesis is that method 1 and method 2 have different levels of accuracy.
}
\references{
Diebold, F.X. and Mariano, R.S. (1995) Comparing predictive accuracy. \emph{Journal of Business
and Economic Statistics}, \bold{13}, 253-263.}

\author{George Athanasopoulos, Yousaf Khan and Rob Hyndman}

\examples{
# Test on in-sample one-step forecasts
f1 <- ets(WWWusage)
f2 <- auto.arima(WWWusage)
accuracy(f1)
accuracy(f2)
dm.test(residuals(f1),residuals(f2),h=1)

# Test on out-of-sample one-step forecasts
f1 <- ets(WWWusage[1:80])
f2 <- auto.arima(WWWusage[1:80])
f1.out <- ets(WWWusage[81:100],model=f1)
f2.out <- Arima(WWWusage[81:100],model=f2)
accuracy(f1.out)
accuracy(f2.out)
dm.test(residuals(f1.out),residuals(f2.out),h=1)
}

\keyword{htest}
\keyword{ts}