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 )