BRUCE2018_FFGN - Fast (exact) fractional Gaussian noise and Brownian motion generator

Usage

y = bruce2018_ffgn(N, tdres, Hinput, noiseType, mu, sigma)

Input parameters

`N`	is the length of the output sequence.
`tdres`	is the time resolution (1/sampling rate)
`Hinput`	is the "Hurst" index of the resultant noise (0 < H <= 2) For 0 < H <= 1,the output will be fractional Gaussian noise with Hurst index H. For 1 < H <= 2, the output will be fractional Brownian motion with Hurst index H-1. Either way, the power spectral density of the output will be nominally proportional to 1/f^(2H-1).
`noiseType`	is 0 for fixed fGn noise and 1 for variable fGn
`mu`	is the mean of the noise. [default = 0]
`sigma`	is the standard deviation of the noise. [default = 1]

Output parameters

`y`	a sequence of fractional Gaussian noise with a mean of zero and a standard deviation of one or fractional Brownian motion derived from such fractional Gaussian noise.

Description

returns a vector containing a sequence of fractional Gaussian noise or fractional Brownian motion. The generation process uses an FFT which makes it very fast.

References:

R. Davies and D. Harte. Tests for hurst effect. Biometrika, 74(1):95 -- 101, 1987.

J. Beran. Statistics for long-memory processes, volume 61. CRC Press, 1994.