Simulation of an FD process with time varying model parameters

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Description

Creates a realization of a time-varying fractionally differenced (FD) process with a given vector of FD parameters and corresponding vector of innovations variances.

Usage

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FDSimulate(delta, innovations.var=1, method="ce", seed=0)

Arguments

delta

a vector containing time-varying FD parameters.

innovations.var

a numeric vector or scalar containing (time-varying) FD innovations variances. If a scalar, the value is replicated appropriately. Otherwise, the length of this input should match the length of the delta vector. Default: 1.

method

a character string defining the method to use in forming the FD realization. Choices are "ce" (circulent emebdding) and "cholesky". Default: "ce".

seed

a positive integer representing the initial seed value to use for the random number generator. If seed=0, the current time is used as a means of generating a (unique) seed value. Otherwise, the specified seed value is used. Default: 0.

Value

a vector containing a (time-varying) FD process realization corresponding to the input FD model parameters.

S3 METHODS

plot

plot the output object. Optional arguments include:

simulation

Plot the simulated series. Default: TRUE.

delta

Plot the FD parameter as a function of time. Default: TRUE.

innovations.var

Plot the innovations variance as a function of time. Default: TRUE.

print

print the output object.

References

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

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

FDWhittle, wavFDPBlock, wavFDPTime.

Examples

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## create a time-varying FD parameter, linearly 
## varying from white to pink noise, then jump 
## to a red noise plateau 
delta <- c(seq(0, 0.5, by=0.01), rep(1,100))

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

## simulate a time-varying FD process 
z <- FDSimulate(delta=delta, innovation=innovation)
print(z)
plot(z)

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