Smooth Seasonal Component of Time Series

Description

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

Usage

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

Arguments

Details

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.

Value

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.

See Also

smooth.basisPar, fd for functional data objects, seasonal.ave for alternative seasonal extraction method.

Examples

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")

Results