acfHKp {HKprocess}

Autocorrelation of HKp

Description

The Hurst-Kolmogorov stochastic process (HKp) is a persistent process. The term HKp is an alternative of the term Fractional Gaussian Noise (FGN, see Koutsoyiannis 2010). Its autocorrelation function (ACF) is given by eq.16 (Koutsoyiannis 2002).

Usage

acfHKp(H, maxlag)

Arguments

H

Hurst parameter

maxlag

ACF computed at lags 0, 1, ..., maxlag

Value

Vector of autocorrelations at lags 0, 1, ..., maxlag.

Note

The parameter H should be in (0, 1), see Koutsoyiannis (2002)

Author(s)

Hristos Tyralis

References

Koutsoyiannis D (2002) The Hurst phenomenon and fractional Gaussian noise made easy. Hydrological Sciences Journal 47(4):573–595. doi:10.1080/02626660209492961.

Koutsoyiannis D (2010) A random walk on water. Hydrology and Earth System Sciences 14:585–601. doi:10.5194/hess-14-585-2010.

Examples

# Compute the ACF at lags 0, 1, ..., 10 when H = 0.8.

acfHKp(0.8, 10)