fArma (version 3010.79)

LongRangeDependence: Statistics of the True LRD Process

Description

A collection and description of functions to investigate the true statistics of the long range dependence or long memory behavior of an univariate time series process. The Functions are: Functions to model the true autocorrelation function and spectrum: ll{ fgnTrueacf Returns true FGN covariances, fgnTruefft returns true FGN fast Fourier transform, fgnStatsSlider returns a plot of true FGN Statistics, farimaTrueacf returns true FARIMA covariances, farimaTruefft returns true FARIMA fast Fourier transform, farimaStatsSlider returns a plot of true FARIMA Statistics. }

Usage

fgnTrueacf(n = 100, H = 0.7) 
fgnTruefft(n = 100, H = 0.7) 
fgnStatsSlider()
farimaTrueacf(n = 100, H = 0.7) 
farimaTruefft(n = 100, H = 0.7)
farimaStatsSlider()

Arguments

H

the Hurst exponent, a numeric value between 0.5 and 1, by default 0.7.

n

number of data points to be simulated, a numeric value, by default 100.

Value

• fgnTrueacf farimaTrueacf return the true covariance of an FGN or FARIMA time series process. fgnTruefft farimaTruefft return the true spectrum of an FGN or FARIMA time series process. fgnStatsSlider() farimStatsSlider() interactively display the true covariance and the true spectrum of an FGN or FARIMA time series process.

Details

Functions to Model True Correlations and Spectrum: The functions fgnTrueacf and farimaTrueacf return the true covariances of an FGN and Gaussian FARIMA(0,d,0) time series process. The functions fgnTruefft and farimaTruefft return the true fast Fourier transform of an FGN and Gaussian FARIMA(0,d,0) time series process. The R functions are implemented from SPlus code written by J. Beran [1994].

References

Beran J. (1992); Statistics for Long-Memory Processes, Chapman and Hall, New York, 1994.

Examples

## fgnTrueacf -
   fgnTrueacf(n = 20, H = 0.8)
   
## fgnTruefft -
   fgnTruefft(n = 20, H = 0.8)
   
## farimaTrueacf -
   farimaTrueacf(n = 20, H = 0.8)
   
## farimaTruefft -
   farimaTruefft(n = 20, H = 0.8)