LrdStatistics: Statistics of the True LRD Process

In fArma: Rmetrics - Modelling ARMA Time Series Processes

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:

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.

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].

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.

Author(s)

J. Beran, ported by Maechler, code as listed in the Appendix of his Book,
Diethelm Wuertz for the Rmetrics R-port.

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)

fArma documentation built on Sept. 9, 2022, 3:02 p.m.