wavelets (version 0.3-0.2)

extend.series: Extend a Time Series

Description

Extends a univariate or multivariate time series beyond its original length.

Usage

extend.series(X, method="reflection", length="double", n, j)

Arguments

X

A univariate or multivariate time series. Numeric vectors, matrices and data frames are accepted.

method

A character string indicating which extension method to use. Possible values are "periodic", "reflection", "zero", "mean", and "reflection.inverse".

length

A character string indicating how to determine the length of the extended series. Possible values are "aribitrary", "powerof2", and "double".

n

An integer value specifying the length of the extended series. This argument is only relevant when length = "arbitrary".

j

An integer value specifying the power of two of which the length of the extended series should be a multiple. This argument is only relevant for length = "powerof2".

Value

The extended time series, in its original class.

Details

The original time series, X, is extended to a new length as determined by length: if length = "arbitrary", a value for the argument n must be specified in order to extend the series to length n; if length = "powerof2" the series will be extended to the nearst multiple of \(2^j\), where j must be specified as an argument to the function; if length = "double" the series will be extended to twice its original length.

Once the length of the extended series is determined, the actual extension is performed using one of five methods: if method = "periodic" a periodic extension is made by concatenating the series with itself (without changing the order of the values); if method = "reflection" an extension is made by concatenating the series with a reflection (reverse ordering) of itself; if method = "zero" the series is padded with zeros; if method = "mean" the series is padded with its mean; if method = "reflection.inverse" an extension is made by concatenating the series with a reflection (reverse ordering) of itself that is further reflected of the horizontal axis \(y = x_N\) where \(x_N\) is the last value of the observed series.

In the case that the series is extended beyond twice it's original length, the "periodic" and "reflection" methods are repetetively applied so that every subseries of length \(N\) (the length of the original series) is either a periodic or reflected extension of any other \(N\) adjacent values. Similarly, the "reflection.inverse" method is repetetively applied so that every \(2N\) values are a periodic extension of any adjacent \(2N\) values.

References

Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

See Also

dwt, modwt.

Examples

# NOT RUN {
# obtain the two series listed in Percival and Walden (2000), page 42
X1 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,.7,.9,0,.3)
X2 <- c(.2,-.4,-.6,-.5,-.8,-.4,-.9,0,-.2,.1,-.1,.1,-.7,.9,0,.3)

# combine them and extend using reflection method
newX <- cbind(X1,X2)
newX.ext1 <- extend.series(newX, length="arbitrary", n=64)
plot.ts(newX.ext1)

# apply another extension method
newX.ext2 <- extend.series(newX, method="reflection.inverse",
                           length="powerof2", j=6)
plot.ts(newX.ext2) 
# }