kernel {ts} | 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.

### Usage

kernel(coef, m, r, name)
df.kernel(k)
bandwidth.kernel(k)
is.tskernel(k)

### Arguments

`coef` |
the upper half of the smoothing kernel coefficients
(inclusive of coefficient zero) *or* the name of a kernel
(currently `"daniell"` , `"dirichlet"` , `"fejer"` or
`"modified.daniell"` . |

`m` |
the kernel dimension. The number of kernel coefficients is
`2*m+1` . |

`name` |
the name of the kernel. |

`r` |
the kernel order for a Fejer kernel. |

`k` |
a `"tskernel"` object. |

### 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).

`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 (1991), p. 201, with a continuity correction.

### Value

`kernel`

returns a list with class `"tskernel"`

, and
components the coefficients `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

data(EuStockMarkets) # Demonstrate a simple trading strategy for the
x <- EuStockMarkets[,1] # financial time series German stock index DAX.
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
data(sunspot) # Reproduce example 10.4.3 from Brockwell and Davies (1991)
spectrum(sunspot.year, kernel=kernel("daniell", c(11,7,3)), log="no")