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HURST
Calculates the Hurst exponent (a measure of persistence or long memory) for a given time series.
Syntax
Hurst(X, Alpha, Return_type)
X
is the input data sample (a one dimensional array of cells (e.g. rows or columns)).
Alpha
is the statistical significance of the test (i.e. alpha). If missing or omitted, an alpha value of 5% is assumed.
Return_type is a number that determines the type of return value: 1 (or missing)=Empirical, 2=(AnisLloyd/Peters) Corrected, 3=Theoretical, 4=Upper Limit, 5=Lower Limit.
RETURN_TYPE  NUMBER RETURNED 

1 or omitted  Empirical Hurst exponent 
2  Corrected Hurst exponent (AnisLloyd/Peters) 
3  Theoretical Hurst exponent (AnisLloyd/Peters) 
4  Upper limit of empirical confidence interval 
5  Lower limit of empirical confidence interval 
Remarks
 The input data series must have at least 9 nonmissing values, or Hurst function returns #VALUE.
 The input data series may include missing values (e.g. #N/A, #VALUE!, #NUM!, empty cell), but they will not be included in the calculations.

The Hurst exponent, , is defined in terms of the Rescaled Range as follows:
Where:
 is the Rescaled Range.
 is the expected value.
 is the time of the last observation (e.g. it corresponds to in the input time series data.)
 is a constant.

The Hurst exponent is a measure of autocorrelation (persistence and long memory).
 A value of indicates a time series with negative autocorrelation (e.g. a decrease between values will probably be followed by another decrease),
 A value of indicates a time series with positive autocorrelation (e.g. an increase between values will probably be followed by another increase),
 A value of indicates a "true random walk", where it is equally likely that a decrease or an increase will follow from any particular value (e.g. the time series has no memory of previous values)
 The Hurst exponent's namesake, Harold Edwin Hurst (18801978), was a British hydrologist who researched reservoir capacity along the Nile river.

The Rescaled Range is calculated for a time series, , as follows:

Calculate the mean:

Create a mean adjusted series:

Calculate the cumulative deviate series Z:

Create a range series R:

Create a standard deviation series R:
Where:
is the mean for the time series values

Calculate the rescaled range series (R/S):

Calculate the mean:
 For time series with less than 96 observations, Hurst function divides the time series of length N into an N8 overlapping time series. Then it computes the scaled ranges for each length.
 For time series with 96 or more, Hurst function divides the time series of full length N into a number of shorter time series of length n = N, N/2, N/4, ... T. then it calculates the scaled range for each length.
 In both cases, the shortest time series is 8 observations.
References
 [1] A.A.Anis, E.H.Lloyd (1976) The expected value of the adjusted rescaled Hurst range of independent normal summands, Biometrica 63, 283298.
 [2] H.E.Hurst (1951) Longterm storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116, 770808.
 [3] E.E.Peters (1994) Fractal Market Analysis, Wiley.
 [4] R.Weron (2002) Estimating long range dependence: finite sample properties and confidence intervals, Physica A 312, 285299.
 Hamilton, J .D.; Time Series Analysis , Princeton University Press (1994), ISBN 0691042896
 Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0471690740