fractal (version 2.0-4)

hurstACVF: Estimate the Hurst coefficient by regression of scaled asinh plot of ACVF vs log(lag)

Description

Estimates long memory parameters beta (ACVF decay exponent), alpha (Equivalent PPL model spectral density exponent), and H (Equivalent Hurst parameter) by linear regression of scaled asinh of ACVF versus log(lag) over intermediate lag values.

Usage

hurstACVF(x, Ascale=1000, lag.min=1, lag.max=64)

Arguments

x

a vector containing a uniformly-sampled real-valued time series.

Ascale

scale factor for use in the scaled asinh plot. Default: 1000.

lag.max

maximum lag for use in linear regression. Default: 64.

lag.min

minimum lag for use in linear regression. Default: 1.

Value

a list with three components:

beta

decay exponent of autocovariance function

alpha

spectral density exponent of equivalent PPL model

H

Hurst exponent for equivalent ACVF decay rate

Details

Evaluates autocovariance function (ACVF) of input time series by call to S-Plus function acf. Constructs sequence asinh(Ascale * ACVF) / asinh(Ascale) and does linear regression (via S-Plus function "lsfit") of this sequence versus log(lag) from lag.min to lag.max. Draws a plot of the sequence and the fit line. Recommended usage: look at resulting plot. Is the intermediate range approximately linear? If plot is too flat, decrease Ascale. If it decreases to zero too quickly, increase Ascale. Values of Ascale from 10 to \(10^6\) have been found useful. If lag.min and lag.max do not bound the range where the sequence is approximately linear then change them and rerun the function to produce a better fit.

References

A. G. Gibbs and D. B. Percival, Forthcoming paper on the autocovariance of the PPL (pure power law) model. A section of the paper discusses the usefulness of scaled asinh plots.

See Also

hurstBlock.

Examples

# NOT RUN {
hurstACVF(wmtsa::nile, Ascale=1000000, lag.min=3, lag.max=68)
# }