kernel {stats} | R Documentation

## Smoothing Kernel Objects

### 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

    kernel(coef, m, 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). 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 Davies (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

    ## 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 Davies (1991)
    spectrum(sunspot.year, kernel=kernel("daniell", c(11,7,3)), log="no")

[Package stats version 2.5.0 Index]