FDSimulate {fractal} | R Documentation

## Simulation of an FD process with time varying model parameters

### 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

    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

    ## 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)

[Package fractal version 1.0-1 Index]