Smoothing Kernel Objects

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Description

The "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 print, plot and [ methods for these kernel objects.

Usage

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

df.kernel(k)
bandwidth.kernel(k)
is.tskernel(k)

## S3 method for class 'tskernel'
plot(x, type = "h", xlab = "k", ylab = "W[k]",
     main = attr(x,"name"), ...)

Arguments

coef

the upper half of the smoothing kernel coefficients (including coefficient zero) or the name of a kernel (currently "daniell", "dirichlet", "fejer" or "modified.daniell".

m

the kernel dimension(s) if coef is a name. When m has length larger than one, it means the convolution of kernels of dimension m[j], for j in 1:length(m). Currently this is supported only for the named "*daniell" kernels.

name

the name the kernel will be called.

r

the kernel order for a Fejer kernel.

k, x

a "tskernel" object.

type, xlab, ylab, main, ...

arguments passed to plot.default.

Details

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 [ method allows natural indexing of kernel objects with indices in (-m) : m. The normalization is such that for k <- kernel(*), sum(k[ -k$m : k$m ]) is one.

df.kernel returns the ‘equivalent degrees of freedom’ of a smoothing kernel as defined in Brockwell and Davis (1991), page 362, and bandwidth.kernel returns the equivalent bandwidth as defined in Bloomfield (1976), p. 201, with a continuity correction.

Value

kernel() returns an object of class "tskernel" which is basically a list with the two components coef and the kernel dimension m. An additional attribute is "name".

Author(s)

A. Trapletti; modifications by B.D. Ripley

References

Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.

Brockwell, P.J. and Davis, R.A. (1991) Time Series: Theory and Methods. Second edition. Springer, pp. 350–365.

See Also

kernapply

Examples

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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")

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