Measuring/Quantifying Divergence

[LS_Chad 10]

I'm often asked if we have an "indicator" for divergence/convergence, and right now, the answer is no. So I'd like to open a thread to discuss how one would measure the divergence between price and any indicator (such as RSI), or between two indicators. In essences, how would you quantify divergence, on a bar to bar basis, between any two series of data points (whether that series be price data, volume data, or any technical indicator values).

 

It is my understanding, that when looking for divergence, you would identify two consecutive significant highs (or significant lows), and look for price increasing between those two bars, while an indicators value decreased (or visa versa).

 

The first question....do we really need a "divergence" value on every bar...or do we only need it on specific bars where these significant highs or lows occurred?

 

And should that divergence just be "true" (we have divergence) or "false" (we don't) or should it have a magnitude?

 

And can we calculate this value over a specific period, or is that period variable? This is what makes measuring/calculating divergence so difficult. It's easy to identify visually on a chart, but trying to put it into code is a different story.

 

I'll begin the discussion by overly simplifying things:

 

Here's an example that uses this custom indicator:

 

(CL > CL.10) * (RSI < RSI.10) - (CL < CL.10) * (RSI > RSI.10)

 

to measure divergence over a 10 bar period between price and RSI on a 3-min chart. The bottom pane shows the custom indicator giving us a value of 1 when we have divergence of price increasing over the 10 bars while RSI decreased, and a value of -1 when price decreased yet RSI increased:

 

http://www.charthub.com/images/2009/03/24/Divergence.png

 

Here's another, that puts some amplitude (change in RSI over 10 bar period) into the value of the histogram (bottom pane):

 

http://www.charthub.com/images/2009/03/24/Divergence_2.png

 

And here is the syntax for that custom indicastor:

 

((RSI.10 - RSI) * (CL > CL.10) * (RSI < RSI.10)) - ((RSI - RSI.10) * (CL < CL.10) * (RSI > RSI.10))

 

Again, I know this overly simplifies the concept, but something we can build on. I'm sure there are a few who have tackled this issue already that could weigh with some good insight.

 

Chad

[Roman 10]

http://www.charthub.com/images/2009/03/25/Diverg_MACD_Ergod

1. Three lines on price pane show price trending down. Some people may dispute the exact placement of those lines, but the fact remains: price declines.

2. The corresponding MACD lows are trending up. May suggest price reversal but not quite. The first declining price trend line is accompanied by a decisive rise in corresponding MACD trend but initially, at least , prices continue to fall. Only the second signal (Dec 8) is followed by price increase.

3. The forth pane shows CI kindly supplied by Chad some time ago -- ergodic signal. The false signal created by MACD -- Price divergence is absent here.

 

The 4 bottom panes are CIs (code provided above by Chad, called "amplified divergence") .

First out of 4 cranks MACD over an arbitrary period of 10 bars.

Second cranks Ergodic over a period of 10 bars.

Third cranks Ergodic over a period of 20 bars.

Forth cranks MACD over a period of 20 bars.

 

 

 

First thing that comes to mind is that the user should be able to adjust the period (number of bars) for analysis. Second: leave the choice of an indicator to the user.

You can slide the dates backward looking at "MACD amplified divergence 20 bars" and spoting former occurrences. The false signal created by "raw" MACD is eliminated.

Third: it allows to quantify the divergence !

[LS_Chad 10]

This subject was covered in the RTL tutorial (and ongoing project) that can be found at:

 

Investor/RT - Tutorial - RTL 101

 

Specifically, the section on Divergence can be found here:

 

Investor/RT - Tutorial - RTL 101

 

Several new functions have been added to RTL which will provide more tools to attack divergence:

 

SLOPE(exp, n) - change-based slope of exp over past n bars: (exp - exp.n)/n

ACCEL(exp, n) - change-based acceleration of exp over past n bars, or slope of current bar minues slope of last bar

SLOPER(exp, n) - regression-based slope of exp over past n bars.

ACCEL(exp, n) - regression based acceleration over past n bars. Difference between the reg-based slope of current bar and reg-based slope of prev bar.

YINT(exp, n) - current value of a regression line through the past n bars of exp

[phase21 10]

Hi Chad,

 

I was interested in your method of determining divergence, but for Trade Navigator, and came up with the following.

 

Original code by Chad:

 

((RSI (Close , BarsToUse , False).(BarsToUse) - RSI (Close , BarsToUse , False)) * (Close > Close.(BarsToUse)) * (RSI (Close , BarsToUse , False) < RSI (Close , BarsToUse , False).(BarsToUse))) - ((RSI (Close , BarsToUse , False) - RSI (Close , BarsToUse , False).(BarsToUse)) * (Close < Close.(BarsToUse)) * (RSI (Close , BarsToUse , False) > RSI (Close , BarsToUse , False).(BarsToUse)))

 

Indicator independent version:

 

(((UserExprOne).(BarsToUse) - (UserExprOne).0) * ((UserExprTwo).0 > (UserExprTwo).(BarsToUse)) * ((UserExprOne).0 < (UserExprOne).(BarsToUse))) - (((UserExprOne).0 - (UserExprOne).(BarsToUse)) * ((UserExprTwo).0 < (UserExprTwo).(BarsToUse)) * ((UserExprOne).0 > (UserExprOne).(BarsToUse)))

 

Example of implementation with chart:

 

TLabQuantDiverg (Regression Value (Close , 7 , 0) , Regression Value (Momentum (Close , 7) , 7 , 0) , 7)

 

 

Note: the use of Regression is merely to smooth-out some of the wrinkle in the input values.

 

Regards,

Edited August 4, 2009 by phase21
Clarification of usage