brainwaver (version 1.6)

const.var.list: Computation of the list of variance vectors

Description

Computes the list of the variance vectors in terms of the scale of the wavelet decomposition.

Usage

const.var.list(data.mat, names.data = 0, method = "modwt", wf = "la8",  n.levels = 4, boundary = "periodic", save.wave = FALSE,  export.data = FALSE)

Arguments

data.mat

matrix containing the data time series. Each column of the matrix represents one time series.

names.data

optional character vector containing the name associated to the column of the matrix data.mat.

method

wavelet decomposition to be used, algorithm implemented in the waveslim package (Whitcher, 2000). By default, the Maximal Overlap Discrete Wavelet Transform is used "modwt". It is also possible to use the classical Discrete Wavelet Transform "dwt".

wf

name of the wavelet filter to use in the decomposition. By default this is set to "la8", the Daubechies orthonormal compactly supported wavelet of length $L=8$ (Daubechies, 1992), least asymmetric family.

n.levels

specifies the depth of the decomposition. This must be a number less than or equal to $log(length(x),2)$.

boundary

Character string specifying the boundary condition. If boundary=="periodic" the default, then the vector you decompose is assumed to be periodic on its defined interval, if boundary=="reflection", the vector beyond its boundaries is assumed to be a symmetric reflection of itself.

save.wave

logical. If TRUE all the wavelet coefficient are saved.

export.data

logical. If TRUE the variance vectors with the upper and lower bound are exported to text file.

Value

Object of class "Wave Variance", basically, a list with the following components

d?

Variance vectors for each scale of the wavelet decomposition.

lowerd?

vector containing the lower bound of the variance for each scale of the wavelet decomposition.

upperd?

vector containing the upper bound of the variance for each scale of the wavelet decomposition.

Details

This function uses the wavelet decomposition implemented in the R package waveslim, (whitcher, 2000).

References

Gencay, R., F. Selcuk and B. Whitcher (2001) An Introduction to Wavelets and Other Filtering Methods in Finance and Economics, Academic Press.

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

S. Achard, R. Salvador, B. Whitcher, J. Suckling, Ed Bullmore (2006) A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs. Journal of Neuroscience, Vol. 26, N. 1, pages 63-72.

See Also

const.cor.list, read.var.txt, save.var.txt

Examples

data(brain)
brain<-as.matrix(brain)

# WARNING : To process only the first five regions
brain<-brain[,1:5]



n.levels<-4
wave.var.list<-const.var.list(brain,n.levels=n.levels)

tot.regions <- dim(brain)[2]
n.series <- dim(brain)[1]

nb.num.regions <- 9
   num.regions <- round(runif(nb.num.regions,2,tot.regions))
    par(mfrow=c(3,3))
    for(k in 1:(nb.num.regions)){
	
        reg <- num.regions[k]

       var.vector<-matrix(0,4,3)
for(i in 1:n.levels){

	var.vector[i,1]<-(wave.var.list[[i]])[reg]
       	var.vector[i,2]<-(wave.var.list[[i+n.levels]])[reg]
       	var.vector[i,3]<-(wave.var.list[[i+2*n.levels]])[reg]
      }
        title <- num.regions[k]
        matplot(2^(0:(n.levels-1)),var.vector,main=title,type="b", 
                log="x", pch="*LU", xaxt="n", lty=1, col=c(1,4,4), 
                xlab="Wavelet Scale",ylab="Wavelet Variance")
        axis(side=1, at=2^(0:7))
        abline(h=0)
      }