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## Weighted generalized Hurst exponent

version 1.1 (2.37 KB) by

Computes the generalized Hurst exponent with exponential weights

Updated

This code calculates the weighted generalized Hurst exponent H(q) from
the scaling of the renormalized q-moments of the distribution

<|x(t+r)-x(t)|^q>_w/<x(t)^q>_w ~ r^[qH(q)]

Here <f>_w are weighted averages of f(t) over 0<= t < T
with weights
w(t) = w0 exp(-(T-t)/delta)
and
w0 = (1-exp(-1/delta))/(1-exp(-T/delta))

H = genhurstw(S)
S is 1xT data series (T>50 recommended)
calculates unweighted H(q=1)

H = genhurstw(S,q)
calculates unweighted H(q) specifying the exponent q
which can be a vector (default value q=1)

H = genhurstw(S,q,delta)
calculates weighted H(q) specifying the characteristic time delta

H = genhurstw(S,q,delta,maxT)
calculates weighted H(q) specifying the characteristic time delta
and the size of the scaling window maxT

[H,sH]=genhurstw(S,...)
estimates the standard deviation sH(q)

examples:
generalized Hurst exponent for a random gaussian process
H=genhurstw(cumsum(randn(10000,1)))
or
H=genhurstw(cumsum(randn(10000,1)),[1,2]) to calculate H(1) and H(2)
or
H=genhurstw(cumsum(randn(10000,1)),[1,2],100) to calculate weighted
H(1) and H(2) with chractreistic time delta = 100

for the generalized Hurst exponent method please refer to:
T. Di Matteo et al. Physica A 324 (2003) 183-188
T. Di Matteo et al. Journal of Banking & Finance 29 (2005) 827-851
T. Di Matteo Quantitative Finance, 7 (2007) 21-36
for the weighted Hurst exponent method please refer to:
R. Morales et al. Physica A, 391 (2012) 3180-3189.