# FDSimulate: Simulation of an FD process with time varying model... In fractal: A Fractal Time Series Modeling and Analysis Package

## 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

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```## 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) ```

### Example output

```Loading required package: splus2R
Loading required package: ifultools
Time Varying FD Process Simulation
----------------------------------
Range delta                  : 0 to 1
Number of unique deltas      : 52
Range innovations variance   : 1 to 1
Number of unique innov. var. : 1
Method                       : circulant embedding
```

fractal documentation built on May 1, 2019, 8:04 p.m.