# 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

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 |

`method` |
a character string defining the method to use in forming the FD realization.
Choices are |

`seed` |
a positive integer representing the initial seed value to use
for the random number generator. If |

### 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 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)
``` |