The most widely accepted techniques to identify long memory are those that can be used to estimate the Hurst exponent
H, which allows to perceive if a given time series follows a (fractional) Brownian motion.
The estimate of the Hurst exponent
(H) takes on a value between 0 and 1.
Further, we seek to ascertain whether each of the returns series studies can be classified as "persistent" or "antipersistent", based on its estimated Hurst exponent
. The study by Hiremath & Kumari (2015) represents another recent assessment of pricing efficiency in the Indian context, and it tests for long memory in both sectoral and broader indices.
MDFA method has been recently preferred to reveal multifractal scaling (Hurst exponent
) characteristics of complex signals (biomedical studies in general) which have nonstationary statistics [27-30].
This set includes Higuchi's fractal dimension (HFD), Hurst exponent
(Hr), and Katz fractal exponent (KATZ).
Stanley, "Time-dependent Hurst exponent
in financial time series," Physica A: Statistical Mechanics and Its Applications, vol.
(2005), "A comment on measuring the hurst exponent
of financial time series", Physica A: Statistical Mechanics and its Applications, Vol.
The structural similarity between the two processes, their predictability and determination of characteristic frequencies was performed with using the relevant statistics, including the so-called Hurst exponent
. An important element of proceeding the threats is the relationship in the domain of extreme events as a decisive influence - the difference compared to traditional analysis.
They include computation of the (i) Correlation Dimension, [d.sub.c]; (ii) Hurst Exponent
, H; (iii) Kolmogorov Entropy, K; and (iv) Largest Lyapunov Exponent (LLE), [[lambda].sub.max].
Since random walk (martingale) is not applicable in this case, we employ the Hurst Exponent
(Hurst, 1951) to test the EMH because it affords a measure for both long-term memory and fractality of a time series, has fewer assumptions about the underlying system, and does not assume a normal distribution.
The generalized Hurst exponent
h(q) and the scaling exponent [tau](q), the singularity exponent [alpha], and the singular spectrum f([alpha]) in multifractal formula have the following relationships: