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% File src/library/stats/man/kernel.Rd

% Part of the R package, https://www.R-project.org

% Copyright 1995-2014 R Core Team

% Distributed under GPL 2 or later

\name{kernel}

\alias{kernel}

\alias{bandwidth.kernel}

\alias{df.kernel}

\alias{is.tskernel}

\alias{plot.tskernel}

\title{Smoothing Kernel Objects}

\description{

  The \code{"tskernel"} class is designed to represent discrete

  symmetric normalized smoothing kernels.  These kernels can be used to

  smooth vectors, matrices, or time series objects.

  There are \code{\link{print}}, \code{\link{plot}} and \code{\link{[}}

  methods for these kernel objects.

}

\usage{

kernel(coef, m = 2, r, name)

df.kernel(k)

bandwidth.kernel(k)

is.tskernel(k)

\method{plot}{tskernel}(x, type = "h", xlab = "k", ylab = "W[k]",

     main = attr(x,"name"), \dots)

}

\arguments{

  \item{coef}{the upper half of the smoothing kernel coefficients

    (including coefficient zero) \emph{or} the name of a kernel

    (currently \code{"daniell"}, \code{"dirichlet"}, \code{"fejer"} or

    \code{"modified.daniell"}).}

  \item{m}{the kernel dimension(s) if \code{coef} is a name.  When \code{m}

    has length larger than one, it means the convolution of

    kernels of dimension \code{m[j]}, for \code{j in 1:length(m)}.

    Currently this is supported only for the named "*daniell" kernels.}

  \item{name}{the name the kernel will be called.}

  \item{r}{the kernel order for a Fejer kernel.}

  \item{k, x}{a \code{"tskernel"} object.}

  \item{type, xlab, ylab, main, \dots}{arguments passed to

    \code{\link{plot.default}}.}

}

\details{

  \code{kernel} is used to construct a general kernel or named specific

  kernels.  The modified Daniell kernel halves the end coefficients (as

  used by S-PLUS).

  The \code{\link{[}} method allows natural indexing of kernel objects

  with indices in \code{(-m) : m}.  The normalization is such that for

  \code{k <- kernel(*)}, \code{sum(k[ -k$m : k$m ])} is one.

  \code{df.kernel} returns the \sQuote{equivalent degrees of freedom} of

  a smoothing kernel as defined in Brockwell and Davis (1991), page

  362, and \code{bandwidth.kernel} returns the equivalent bandwidth as

  defined in Bloomfield (1976), p.\sspace{}201, with a continuity correction.

}

\value{

  \code{kernel()} returns an object of class \code{"tskernel"} which is

  basically a list with the two components \code{coef} and the kernel

  dimension \code{m}.  An additional attribute is \code{"name"}.

}

\author{A. Trapletti; modifications by B.D. Ripley}

\seealso{

    \code{\link{kernapply}}

}

\references{

  Bloomfield, P. (1976)

  \emph{Fourier Analysis of Time Series: An Introduction.}

  Wiley.

  Brockwell, P.J. and Davis, R.A. (1991)

  \emph{Time Series: Theory and Methods.}

  Second edition. Springer, pp.\sspace{}350--365.

}

\examples{

require(graphics)

## Demonstrate a simple trading strategy for the

## financial time series German stock index DAX.

x <- EuStockMarkets[,1]

k1 <- kernel("daniell", 50)  # a long moving average

k2 <- kernel("daniell", 10)  # and a short one

plot(k1)

plot(k2)

x1 <- kernapply(x, k1)

x2 <- kernapply(x, k2)

plot(x)

lines(x1, col = "red")    # go long if the short crosses the long upwards

lines(x2, col = "green")  # and go short otherwise

## More interesting kernels

kd <- kernel("daniell", c(3, 3))

kd # note the unusual indexing

kd[-2:2]

plot(kernel("fejer", 100, r = 6))

plot(kernel("modified.daniell", c(7,5,3)))

# Reproduce example 10.4.3 from Brockwell and Davis (1991)

spectrum(sunspot.year, kernel = kernel("daniell", c(11,7,3)), log = "no")

}

\keyword{ts}