\name{Arima}
\alias{Arima}
\title{Fit ARIMA model to univariate time series}
\usage{
Arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA),
      xreg = NULL, include.mean = TRUE, include.drift = FALSE, 
      transform.pars = TRUE, fixed = NULL, init = NULL, 
      method = c("CSS-ML", "ML", "CSS"), n.cond, 
      optim.control = list(), kappa = 1e6, model=NULL)
}

\arguments{
\item{x}{a univariate time series}
\item{order}{A specification of the non-seasonal part of the ARIMA model: the three components (p, d, q) are the AR order, the degree of differencing, and the MA order.}
\item{seasonal}{A specification of the seasonal part of the ARIMA model, plus the period (which defaults to frequency(x)). This should be a list with components order and period, but a specification of just a numeric vector of length 3 will be turned into a suitable list with the specification as the order.}
\item{xreg}{Optionally, a vector or matrix of external regressors, which must have the same number of rows as x.}
\item{include.mean}{Should the ARIMA model include a mean term? The default is TRUE for undifferenced series, FALSE for differenced ones (where a mean would not affect the fit nor predictions).}
\item{include.drift}{Should the ARIMA model include a linear drift term? (i.e., a linear regression with ARIMA errors is fitted.) 
    The default is FALSE.}
\item{transform.pars}{Logical. If true, the AR parameters are transformed to ensure that they remain in the region of stationarity. Not used for method = "CSS".}
\item{fixed}{optional numeric vector of the same length as the total number of parameters. If supplied, only NA entries in fixed will be varied. transform.pars = TRUE will be overridden (with a warning) if any AR parameters are fixed. It may be wise to set transform.pars = FALSE when fixing MA parameters, especially near non-invertibility.}
\item{init}{optional numeric vector of initial parameter values. Missing values will be filled in, by zeroes except for regression coefficients. Values already specified in fixed will be ignored.}
\item{method}{Fitting method: maximum likelihood or minimize conditional sum-of-squares. The default (unless there are missing values) is to use conditional-sum-of-squares to find starting values, then maximum likelihood.}
\item{n.cond}{Only used if fitting by conditional-sum-of-squares: the number of initial observations to ignore. It will be ignored if less than the maximum lag of an AR term.}
\item{optim.control}{List of control parameters for optim.}
\item{kappa}{the prior variance (as a multiple of the innovations variance) for the past observations in a differenced model. Do not reduce this.}
\item{model}{Output from a previous call to \code{Arima}. If model is passed, this same model is fitted to
\code{x} without re-estimating any parameters.}
}

\description{Largely a wrapper for the \code{\link[stats]{arima}} function in the stats package. The main difference is that this function
allows a drift term. It is also possible to 
take an ARIMA model from a previous call to \code{Arima} and re-apply it to the data \code{x}.
}
\details{See the \code{\link[stats]{arima}} function in the stats package.}

\value{See the \code{\link[stats]{arima}} function in the stats package. The additional objects returned are
\item{x}{The time series data}
\item{xreg}{The regressors used in fitting (when relevant).}
}

\seealso{\code{\link[stats]{arima}}}

\author{Rob J Hyndman}
\examples{fit <- Arima(WWWusage,order=c(3,1,0))
plot(forecast(fit,h=20))

air.model <- Arima(AirPassengers[1:100],c(0,1,1))
air.model2 <- Arima(AirPassengers,model=air.model)
outofsample <- ts(fitted(air.model2)[-c(1:100)],s=1957+4/12,f=12)
}
\keyword{ts}