\name{mean.fts}
\alias{mean.fts}
\title{Mean functions for functional time series}
\description{
Computes mean of functional time series at each variable.
}
\usage{
\method{mean}{fts}(x, method = c("coordinate", "FM", "mode", "RP", "RPD", "radius"), 
 na.rm = TRUE, alpha, beta, weight, ...)
}
\arguments{
\item{x}{An object of class \code{fts}.}
\item{method}{Method for computing the mean function.}
\item{na.rm}{A logical value indicating whether NA values should be stripped before the computation proceeds.}
\item{alpha}{Tuning parameter when \code{method="radius"}.}
\item{beta}{Trimming percentage, by default it is 0.25, when \code{method="radius"}.}
\item{weight}{Hard thresholding or soft thresholding.}
\item{...}{Other arguments.}
}
\details{
If \code{method = "coordinate"}, it computes the coordinate-wise functional mean.

If \code{method = "FM"}, it computes the mean of trimmed functional data ordered by the functional depth of Fraiman and Muniz (2001).

If \code{method = "mode"}, it computes the mean of trimmed functional data ordered by \eqn{h}-modal functional depth.

If \code{method = "RP"}, it computes the mean of trimmed functional data ordered by random projection depth.

If \code{method = "RPD"}, it computes the mean of trimmed functional data ordered by random projection derivative depth.

If \code{method = "radius"}, it computes the mean of trimmed functional data ordered by the notion of alpha-radius. 
}
\value{A list containing \code{x} = variables and \code{y} = mean rates.}
\references{
O. Hossjer and C. Croux (1995) "Generalized univariate signed rank statistics for testing and estimating a multivariate location parameter", \emph{Journal of Nonparametric Statistics}, \bold{4}(3), 293-308.

A. Cuevas and M. Febrero and R. Fraiman (2006) "On the use of bootstrap for estimating functions with functional data", \emph{Computational Statistics \& Data Analysis}, \bold{51}(2), 1063-1074.

A. Cuevas and M. Febrero and R. Fraiman (2007), "Robust estimation and classification for functional data via projection-based depth notions", \emph{Computational Statistics}, \bold{22}(3), 481-496.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2007) "A functional analysis of NOx levels: location and scale estimation and outlier detection", \emph{Computational Statistics}, \bold{22}(3), 411-427.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2008) "Outlier detection in functional data by depth measures, with application to identify abnormal NOx levels", \emph{Environmetrics}, \bold{19}(4), 331-345.

M. Febrero and P. Galeano and W. Gonzalez-Manteiga (2010) "Measures of influence for the functional linear model with scalar response", \emph{Journal of Multivariate Analysis}, \bold{101}(2), 327-339. 

J. A. Cuesta-Albertos and A. Nieto-Reyes (2010) "Functional classification and the random Tukey depth. Practical issues", Combining Soft Computing and Statistical Methods in Data Analysis, Advances in Intelligent and Soft Computing, Volume 77, 123-130.

D. Gervini (2012) "Outlier detection and trimmed estimation in general functional spaces", \emph{Statistica Sinica}, \bold{22}(4), 1639-1660.
}
\author{Rob J Hyndman, Han Lin Shang}
\seealso{\code{\link[ftsa]{median.fts}}, \code{\link[ftsa]{var.fts}}, \code{\link[ftsa]{sd.fts}}, \code{\link[ftsa]{quantile.fts}}}
\examples{
# Calculate the mean function by the different depth measures.	
mean(x = ElNino, method = "coordinate")
mean(x = ElNino, method = "FM")
mean(x = ElNino, method = "mode")
mean(x = ElNino, method = "RP")
mean(x = ElNino, method = "RPD")
mean(x = ElNino, method = "radius", alpha=0.5, beta=0.25, weight="hard")
mean(x = ElNino, method = "radius", alpha=0.5, beta=0.25, weight="soft")
}
\keyword{methods}