A Statistical Study of the Wells Wilder Index

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 Sciences2School of Physics, Trinity College Dublin

Summary

What’s the Wells Wilder index?How it’s computed and used by technical traders

Aspects analyzedFrequency of price gains and lossesAims 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

Calculation of Wells Wilder Index (WWI) (also, known as RSI – Relative Strength Index)

RSI=100− 1001+RS RS=

EMA (𝑢𝑖)EMA (𝑑𝑖)

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.

close𝑖− close𝑖− 1=∆ 𝑃 𝑖

if ∆ 𝑃 𝑖>0𝑢𝑖=∆ 𝑃 𝑖 ,𝑑𝑖=0if ∆ 𝑃 𝑖<0𝑢𝑖=0 ,𝑑𝑖=|∆ 𝑃 𝑖|

𝛼=2 /(𝑇+1)

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.

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.

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.

Examples of Wells Wilder Index for Dow Jones data

Dow Jones and WWI (RSI) distributions

S&P 500 and WWI (RSI) distributions

Does it actually work? Does it make money?

(Dow Jones index)

A detailed view.Trading between

1200000 and 1202000 minutes

(3 hours and 2 minutes)

Does it work for S&P 500?

S&P 500a detailed

view of the trading

Would you like to bet your money?Thank you!