How to estimate Hurst exponent?
To estimate the Hurst exponent, one must first estimate the dependence of the rescaled range on the time span n of observation. A time series of full length N is divided into a number of shorter time series of length n = N, N/2, N/4, The average rescaled range is then calculated for each value of n.
What is generalized Hurst exponent?
Thus, the generalized Hurst exponent H (q) describes the long-memory dependence or persistence in the original signal S (t). As a general rule, when H (q) >0.5, the signal fluctuations related to the order q are persistent. When H (q) <0.5, the signal fluctuations related to the order q are anti-persistent.
How is Hurst component calculated?
Rescaled Range and the Hurst Exponent The rescaled range is calculated by dividing the range (maximum value minus minimum value) of the cumulative mean adjusted data points (sum of each data point minus the mean of the data series) by the standard deviation of the values over the same portion of the time series.
What does mean reverting mean?
Mean reversion, or reversion to the mean, is a theory used in finance that suggests that asset price volatility and historical returns eventually will revert to the long-run mean or average level of the entire dataset.
How is the Hurst exponent calculated in hurstexp?
hurstexp (x) calculates the Hurst exponent of a time series x using R/S analysis, after Hurst, with slightly different approaches, or corrects it with small sample bias, see for example Weron. These approaches are a corrected R/S method, an empirical and corrected empirical method, and a try at a theoretical Hurst exponent.
How is the Hurst function estimating long range dependence?
R.Weron (2002) Estimating long range dependence: finite sample properties and confidence intervals, Physica A 312, 285-299.
Which is the optimal sample size for Hurst function?
Optimal sample sizes are automatically computed with a length that possesses the most divisors among series shorter than x by no more than 1 percent. H.E.Hurst (1951) Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116, 770-808.