Description Usage Arguments Details Value See Also Examples

Extracts seasonal component of time series by fitting the data with a linear combination of smooth periodic functions.

1 | ```
seasonal.smooth(x, basis = create.fourier.basis(nbasis = 3), lambda = 0, ...)
``` |

`x` |
A univariate time series. |

`basis` |
A functional basis object (see |

`lambda` |
A nonnegative number specifying the amount of smoothing. By default, apply no additional smoothing. |

`...` |
Not currently used. |

Although it is possible to specify arbitrary functional basis object,
the function will only work properly if the basis is periodical on the
unit interval. It is recommended to use a Fourier basis with default
period (`create.fourier.basis`

).

Positive values of `lambda`

imply a restriction on roughness of
the result. The more the value, the more smooth result is; see
`smooth.basis`

for more detailed description.

A time series object with times from 0 to 1 and the same frequency as
`x`

. The smoothing functional data object is stored in attribute
`fd`

.

`smooth.basisPar`

, `fd`

for
functional data objects, `seasonal.ave`

for alternative
seasonal extraction method.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 | ```
set.seed(19860306)
## Artificial example
x <- ts(sin(2*pi*(3:97)/10) + 0.5*rnorm(length(3:97)),
start = c(0, 3), frequency = 10)
fourier3 <- seasonal.smooth(x)
fourier9 <- seasonal.smooth(x, create.fourier.basis(nbasis = 9))
fourier9s<- seasonal.smooth(x, create.fourier.basis(nbasis = 9), 1E-6)
plot.default(time(x)%%1, x, xlab = "Phase")
points(fourier3, pch = 20, col = "blue")
lines(attr(fourier3, "fd"), col = "blue")
points(fourier9, pch = 20, col = "green")
lines(attr(fourier9, "fd"), col = "green")
points(fourier9s,pch = 20, col = "red")
lines(attr(fourier9s, "fd"),col = "red")
legend("bottomleft",
legend = c("Fourier-3 basis",
"Fourier-9 basis",
"Fourier-9 basis, smooth"),
col = c("blue", "green", "red"),
lty = "solid")
## Realistic example
data(nesterov.index, package = "mar1s")
x <- log(nesterov.index[, "mean"])
x[x < -10] <- -Inf
fourier3 <- seasonal.smooth(x)
fourier9 <- seasonal.smooth(x, create.fourier.basis(nbasis = 9))
fourier9s<- seasonal.smooth(x, create.fourier.basis(nbasis = 9), 2E-5)
plot.default(time(x)%%1, x, xlab = "Phase", pch = ".")
lines(attr(fourier3, "fd"), col = "blue")
lines(attr(fourier9, "fd"), col = "green")
lines(attr(fourier9s,"fd"), col = "red")
legend("topleft",
legend = c("Fourier-3 basis",
"Fourier-9 basis",
"Fourier-9 basis, smooth"),
col = c("blue", "green", "red"),
lty = "solid")
``` |

```
Loading required package: cmrutils
Loading required package: chron
Loading required package: fda
Loading required package: splines
Loading required package: Matrix
Attaching package: 'fda'
The following object is masked from 'package:graphics':
matplot
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
```

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