Trader's Roundtable

[sagev]

In another post there's a quote from William Eckhardt,

[LeviF]

This is a dusty old post, but I'm curious as well.

[sluggo]

I suppose if you want to get all math-ey about it, anything with an exponent other than 1.00 is, mathematically, nonlinear. Thus, for example, any application of Fractals and/or Hurst Exponents (which are around 0.5 or thereabouts) to price historical data, will have an exponent that isn't 1.00 and so it will be nonlinear.

Another common technical analysis tool which uses an exponent other than 1.00 is the Coefficient of Determination, also called R squared: http://www.tradingblox.com/forum/viewtopic.php?p=27086&highlight=%2Asquare%2A#27086 In effect, it measures what's left over after all the linearity is removed. Which, if you think about it, might be a pretty fair definition of non-linear.

But my guess is that Eckhardt wasn't actually talking about exponents. My guess is, he was talking about the (nonlinear) operators MAX and MIN. These are not linear functions of the input data, in fact, they are pathological functions of the input data since they completely disregard almost all of the input data. Into the discard bin, the garbage can, the trash heap, with a hearty Hock Ptui! and a dismissive wave.

Math weenies will recognize the "MAX" function as the limit, as p approaches infinity, of the p-Norm of a vector (see (wikipedia) for more). And so we can say that the MAX function is nonlinear because it involves an exponent that is not equal to 1.00 ... the exponent is infinity. Same goes for MIN.

Bill Rempel might wish to expand upon these sketchy descriptions.

[AFJ Garner]

Ah, right. That's, er, really cleared that one up for me then!

[danZman]

[jungle]

Google "linear function" (or "nonlinear function").

The definition of a linear function f(x), courtesy of Wikipedia, is:
f(x+y)=f(x)+f(y) and f(ax)=af(x). O.w. the function is nonlinear.

[sluggo]

Translation: We here at Eckhardt System Development Labs, avoid the Blox functions "Average" and "EMA" as we feel they have been mined dry. We much prefer the Blox functions "Highest" and "Lowest".

We also avoid Blox functions that use "Average" and "EMA" in their internal calculations, such as RSI, MACD, etc.

[AFJ Garner]

Many thanks. That's much better!

[paloma]

You da man Sluggo!

[LeviF]

Interesting.

[Asamat]

Trying to translate the implications of the term non-linearity from mathematics to ordinary language:

Linear systems are easier to unterstand and predict, because small changes of anything usually lead to small changes in the results. If you have a working system using an EMA, it should work similarly with an SMA. A not overoptimzed system using an SMA(20) should work similarly with an SMA(21). If a 3.0 ATR stop works for you, a 3.2 stop should give not much different results.

Non-linear systems are different in that small changes may lead to vastly different result. Chaotic systems are non-linear, for example the proverbial butterfly effect. Another exmple is filling a balloon. At first it behaves linearly: putting in a bit more air leads to a bit larger volume. Eventually the linearity breaks down, when the balloon bursts. The last additional bit of air caused a vastly different behaviour compared to all the earlier ones.

Since linear systems are far easier to study, mostly those are the systems that are studied. That holds for mathematics, physics, econometric, and trading systems.

Regards,
Asamat

[adamant]

I found this thread very interesting and would really appreciate any links to reading material on the topic of non-linear vs linear trading systems. Also, I would venture to ask Sluggo or other experienced forum members what their opinions are with regard to the accuracy of Eckhardt's (Not Simons) statement.

[sluggo]

I think you've got a dangling reference (link1) (link2) since the character string "simons" is mentioned in your post but nowhere else in this thread.

[LeviF]

Lol. I also did a page search for "simons" after reading this post.

[adamant]

Sorry guys You are abolutely right. Mixed up the names....so many gurus, one tiny goldfish brain

[sluggo]

[LeviF]

From time to time I still get the urge to search for the holy grail - that magic indicator that will be right 100% of the time with no losses, allow me to pick tops/bottoms, etc. But those urges are beginning to wane.

There either isnt a holy grail or I havent been able to find it. Looking at professional manager's returns, it doesnt appear many of them have found it either.

For now, I will ignore linear this, non-linear that, and continue to follow trends and manage risk...

[alp]

From the other thread:

[adamant]

Thanks. Though I am a newbie to systems trading, I am not on a mission for a holy grail. I just think it's interesting to hear people's opinions on various topics, since you all usually have interesting things to say (no exception this time). This in turn may help me on my way, or not.

[sluggo]

Another example of a nonlinear function that's often used in indicators and trading systems: MEDIAN. Sorry I didn't remember to mention it earlier.

MAX, MIN, STDEV, MEDIAN, RSQUARED, ROOTMEANSQUARE, ...

These fall into two classes:

• those which involve sorting the data and then operating upon a selected subset (max, min, median)
  
  
• those involving exponents other than 1 (stdev, rsq, rms)

Not to say that there aren't more