Generate the weights for a time-varying FD process simulation.

USAGE:

wavFDPSimulateWeights( delta = c(0.2, 0.4), innovation = rep(1,2) )

DESCRIPTION:

Time varying fractionally differenced (FD) process realizations are generated by cumulatively summing over the inner product of a Gaussian pseudo-random noise sequence (with zero mean and unit variance) and a series of weights that are dependent upon both the FD parameter. and innovations variance at a particular time. This function generates these weights and returns them in a matrix.

REQUIRED ARGUMENTS:

delta
A vector containing time-varying FD parameters.

OPTIONAL ARGUMENTS:

innovations.variance
A vector containing time-varying FD innovations variances. Default: a vector the same length as delta and filled with ones.

VALUE:

result
A lower triangular matrix containing the weights needed to simulate a time-varying FD process realization corresponding to the input FD model parameters. The weights needed to simulate the t-th point of a time-varying FD process realization are located in result[t,1:t].

REFERENCES:

(1) D. B. Percival and A. T. Walden, ``Wavelet Methods for Time Series Analysis'', Cambridge University Press, 2000.

(2) D. B. Percival and W.L.B. Constantine, ``Exact Simulations of Time-Varying Fractionally Differenced Processes'', submitted to Journal of Computational and Graphical Statistics, 2002.

SEE ALSO:

, , .

EXAMPLES:

    ## create a time-varying FD parameter,
    ## linearly varying from white to pink noise
    delta <- seq( 0, 0.5, by = 0.02 )

    ## set the innovations variance to unity
    innovation <- rep(1, length( delta ) )

    ## creates the weights needed to simulate a
    ## time-varying FD process
    result <- wavFDPSimulateWeights( delta = delta,
    + innovation = innovation )