Hurst exponent

Stock Market - Uptrend, Downtrend Or Random

A general approach to market analysis (market return and stock prices) is to assume the underlying distribution to be normal. But in reality this is not the case due to

many factors like sudden change of interest rate, business cycles and political climates, investors trading preferences and etc. Accordingly, the return of stock prices

and market index is not random and the normal distribution does not reflect the actual distribution.

Rescaled Range analysis is a statistical methodology used to detect the presence or absence of trend in time series by finding the Hurst exponent. For example, it is

generally known that time series like stock prices, indexes of stock market, sunspot etc does exhibit the persistence of trends. R/S analysis is also highly data intensive.

Basically, this method is used to identify when a stock price is persistence i.e. the tendency of the price to continue its current direction and also antipersistence i.e. the

tendency of the price to reverse itself rather than to continue its current direction. Or it is random and unpredictable.

The Hurst exponent is use to determine the underlying distribution of a particular time series. As a rule of thumb...

a) 0.50 < H < 1.0 implies a persistence time series. The larger the H indicates a stronger trend. (strong position on long or short)

b) 0 < H < 0.5 implies antipersistence. (trade on reversal)

c) H more or less equal to 0.5 indicates random time series. (No position taken)

(A complete explanation on how the Hurst exponent is calculated is available at this link)

R/S Analysis is also use to find the primary cycle length of stock prices and market indexes. The V Statistic shown below is very efficient in doing this. Not only the

primary cycle but the underlying cycle as well, as long as the subcycles is a small, finite number.

Two charts will be generated in the Report sheet :

1) R/S Chart - Hurst exponent can be approximated by plotting the Log (R/S) against the Log (N) by solving the slope ( y,x ). ( see screenshot )

2) V Statistic Chart - the break at point A in this chart can be used the estimate the cycle length - find the antilog of point A. ( see screenshot )

( NOTE: If the time series is antipersistence, i.e., H < 0.5 then it will be a upward slope.)

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User Guide :

1) Open KaotiXL.xla

2) Enter the time series in the Data Range box.

3) By default, KaotiXL use period 5 (N) to start calculation. User can enter different period (N).

4) Select what type of data to process i.e Original data or the Return

5) If user select the Return data to process, KaotiXL will automatically process the original data using this equation ( N+1- N ); N = period

6) Click on the Run button to start calculation

7) User can stop the program prematurely by clicking the Abort button. No report will be generated if this option is chosen.

8) End program by clicking the Cancel button.

9) Report shown below will be generated. (Note: User will need to rename or delete worksheet if Report reach to number 10)

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