Kareen Omer, Oleg Yordanov and Peter Richmond – A Statistical Study of the Wells Wilder Index (Talk at 2nd Annual KNOWeSCAPE Scientific Meeting, http://knowescape.org/knowescape2014-2/)

1. A brief look at the statistical character of the
Wells Wilder Index
Kareem Omar1, Oleg Yordanov1 and Peter Richmond2
1Institute of Electronics, Bulgarian Academy of
Sciences
2School of Physics, Trinity College Dublin

2. Summary
What’s the Wells Wilder index?
How it’s computed and used by technical traders
Aspects analyzed
Frequency of price gains and losses
Aims to answer holy grail question: when to buy when to sell!!!
Does it actually work? Does it make money? And in
particular for high-frequency financial data

3. Calculation of Wells Wilder Index (WWI)
(also, known as RSI – Relative Strength Index)
close푖 − close푖−1 = Δ푃푖
if Δ푃푖 > 0 푢푖 = Δ푃푖 , 푑푖 = 0
if Δ푃푖 < 0 푢푖 = 0, 푑푖 = Δ푃푖
RSI = 100 −
100
1 + RS
RS =
EMA(푢푖 )
EMA(푑푖 )
훼 = 2/(푇 + 1)
The RSI varies between 0 and 100.
The values of 30 and 70 are used as markers to buy and sell, respectively.
Other values are also used, such as 20 and 80, or 10 and 90.

4. Important: Marcel’s work
Marcel published in 1998 a paper in PRE of using moving average
on synthetic time series that are akin to financial data.

5. Data used: Dow Jones Industrial Average (INDU)
Minute by minute data
during the trading periods
between 09:30 AM and
16:00 PM. The data span
April 01, 1993 --- August
05, 2011, glued together
for a total of 1 777 197
data points.

6. Data used: S&P500 (INX)
Minute by minute data
during the trading periods
between 10:00 AM and
16:00 PM. The data span
February 01, 1983 ---
August 05, 2011, glued
together for a total of
2 679 048 data points.

7. Examples of Wells Wilder Index for Dow Jones data

8. Dow Jones and WWI (RSI) distributions

9. S&P 500 and WWI (RSI) distributions

10. Does it actually work?
Does it make money?
(Dow Jones index)

11. A detailed view.
Trading between
1200000 and
1202000 minutes
(3 hours and 2
minutes)

12. Does it work
for S&P 500?

13. S&P 500
a detailed
view of the
trading

14. Would you like to bet your money?
Thank you!