costat (version 1.1-1)

coeftofn: Convert wavelet coefficients for two time-varying functions into two functions with respect to time.

Description

In much of the costationarity code the combination functions are represented in terms of wavelet coefficients. At certain points the actual combination functions themselves are required (in the time domain) for purposes such as actually forming the linear combination. This function turns the coefficients, for the two combination functions, into their time domain functional representation.

Usage

coeftofn(alpha, beta, n = 256, filter.number = 1, family = "DaubExPhase")

Arguments

alpha

One set of coefficients for one of the combination functions

beta

The other set of coefficients

n

The length of resulting function that you require

filter.number

The type of wavelet (the number of vanishing moments)

family

The type of wavelet (the wavelet family)

Value

• A list containing two components:
• alpha
  A vector, of length n, containing one of the time-varying combination functions
• beta
  Same as alpha, but contains the other combination function.

Details

A degree of efficiency is built into the code. Typically, for forming stationary linear combinations then only a few (or at least a medium number) of coarser scale coefficients need to be manipulated (eg modified in the optimizer). However, the actual length of the function (time series length) is typically much longer (e.g. n=256, n=512, or higher). So, this function pads out the small number of coarse coefficients with zeros before forming the combination functions which end up at the correct length, n.

References

`Costationarity and stationarity tests for stock index returns' by Cardinali and Nason.

See Also

LCTS, LCTSres

Examples

#
# Very artifical example
#
tmp.a <- c(1, -1)
tmp.b <- c(0.5, 0.5)
#
#
#
ans <- coeftofn(tmp.a, tmp.b)
#
# Should return two combination functions of length 256
#
length(ans$alpha)
#[1] 256