Simulation of an FD process with time varying model parameters
Creates a realization of a time-varying fractionally differenced (FD) process with a given vector of FD parameters and corresponding vector of innovations variances.
FDSimulate(delta, innovations.var=1, method="ce", seed=0)
a vector containing time-varying FD parameters.
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
a character string defining the method to use in forming the FD realization.
a positive integer representing the initial seed value to use
for the random number generator. If
a vector containing a (time-varying) FD process realization corresponding to the input FD model parameters.
plot the output object. Optional arguments include:
Plot the simulated series. Default:
Plot the FD parameter as a function of time. Default:
Plot the innovations variance as a function of time. Default:
print the output object.
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.
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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)