Simulates FGN

Description

A fractional Gaussian noise time series is simulated.

Usage

SimulateFGN(n, H)

Arguments

Details

The FFT is used so it is most efficient if you select n to be a power of 2.

Value

vector of length containing the simulated time series

Author(s)

A.I. McLeod

References

Davies, R. B. and Harte, D. S. (1987). Tests for Hurst Effect. Biometrika 74, 95–101.

McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007). Algorithms for Linear Time Series Analysis, Journal of Statistical Software.

See Also

DLSimulate

Examples

#Example 1
#simulate a process with H=0.2 and plot it
z<-SimulateFGN(100, 0.2)
ts.plot(z)
# 
#Example 2
#simulate FGN and compare theoretical and sample autocovariances
H<-0.7
n<-8192
z<-SimulateFGN(n, H)
#autocovariances
sacvf<-acf(z, plot=FALSE,type="covariance")$acf
tacf<-acvfFGN(H, n-1)
tb<-matrix(c(tacf[1:10],sacvf[1:10]),ncol=2)
dimnames(tb)<-list(0:9, c("Tacvf","Sacvf"))
tb

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(FGN)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FGN/SimulateFGN.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SimulateFGN
> ### Title: Simulates FGN
> ### Aliases: SimulateFGN
> ### Keywords: ts datagen
> 
> ### ** Examples
> 
> #Example 1
> #simulate a process with H=0.2 and plot it
> z<-SimulateFGN(100, 0.2)
> ts.plot(z)
> # 
> #Example 2
> #simulate FGN and compare theoretical and sample autocovariances
> H<-0.7
> n<-8192
> z<-SimulateFGN(n, H)
> #autocovariances
> sacvf<-acf(z, plot=FALSE,type="covariance")$acf
> tacf<-acvfFGN(H, n-1)
> tb<-matrix(c(tacf[1:10],sacvf[1:10]),ncol=2)
> dimnames(tb)<-list(0:9, c("Tacvf","Sacvf"))
> tb
       Tacvf      Sacvf
0 1.00000000 0.98452661
1 0.31950791 0.30091562
2 0.18875254 0.18437728
3 0.14617344 0.14359213
4 0.12249870 0.13051916
5 0.10695009 0.09633975
6 0.09577227 0.09786651
7 0.08725940 0.09469912
8 0.08050989 0.08625907
9 0.07499683 0.06619184
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>