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
The study uses descriptive statistics, ADF and PP test, Hurst exponent
co-integration model, and figures to investigate the normality, stationarity, long memory features, and long-term relationship stability of sample currencies against USD.
c]; (ii) Hurst Exponent
, H; (iii) Kolmogorov Entropy, K; and (iv) Largest Lyapunov Exponent (LLE), [[lambda].
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.
This edition contains a new chapter on volatility in oil prices and manufacturing activity: an investigation of real options, and another on the Hurst exponent
in energy futures prices.
In this paper I present the methodology of determining the Hurst exponent
for market indices.
The existence of memory in the process is based on the value of the Hurst exponent
v], where the scaling (roughness) exponent (H), also called the Hurst exponent
, is given by the relationship:
The time series obtained were subjected to various analyses, namely the correlation function, nonlinear prediction graphs and calculation of the Hurst exponent
, all of which were performed using the specialist software package Chaos Data Analyzer.
The Hurst exponent
can then be estimated (Briens et al.
The processes, called fractional Brownian motions (fBm), enable us to do that on the basis of the fitted Hurst exponent
H (0 < H < 1) over the time interval of interest .
Calculations for the Hurst exponent
(Peters, 1996) resulted in an H value for the price index of 0.