Laguerre ECO (Ergodic Candle Oscillator) Indicator

Posted on September 23rd, 2009
Written by Richard
Posted in: N/A (old archives)

As I’ve mentioned in the blog comments recently, I’m going to start releasing some indicators here for free.

Today’s indicator is: The Laguerre ECO!

ES 12-09 9_23_2009 (6765 Volume)

Idea Behind the Indicator

Most indicators out there run on bars. Let’s take a 3-period moving average. You compute it on the Close, the previous Close, and the Close before that. Well, what if you used 3 other values in your average, instead of the last three prices? Like, what if you used the current value of the 2-EMA, 5-EMA, and 8-EMA and computed the average of those instead?

Well, that’s kind of what Ehlers was wondering in his book, Cybernetic Analysis for Stocks and Futures. His example “time-warps” the data with an all-pass filter based on Laguerre Polynomials, but I think it’s easier for mere mortals to visualize the concept in terms of the EMA’s I described above.

Ehlers uses the 4-RSI as an example application of the Laguerre treatment. Instead of the last 4 Closes, he uses 4 Laguerre values. Using only four values makes the indicator turn quickly, but you can adjust the overall speed of the output via the gamma input to the transform. Pretty neat!

In July, I looked around briefly to see what other Laguerre indicators were out there. Surprisingly, I couldn’t find any. I thought that was strange, because all you have to do is plug in the Laguerre values you need and see what happens. I coded up a few, and found the the Ergodic Candle Oscillator looked pretty good Laguerre-ized.

Some Screenshots

Here’s the Laguerre ECO next to the standard ECO with similar settings. The first thing that impressed me was that, finally, you could use the ECO the way it was intended! If you read Blau’s book, the “safe” long entries are when the ECO is above zero and heading up. In practice, I’ve always found that waiting for the zero cross took too long. The Laguerre version seems to get over the zero line much quicker in some cases (click to enlarge):

ECO_Compare

With the gamma input, you have nice control over the speed of Laguerre indicators. Here’s the ECO running at speeds 0.3, 0.6, and 0.9. What’s cool is that, in all cases, it’s a 4-bar ECO… it’s just time warped by different amounts:

ECO_Speed

Here’s the indicator on a 1 tick, 3-box reversal PnF chart, with a 0.3 and 0.7 Laguerre ECO. I use the longer 0.7 ECO as a filter for zero-cross trades on the 0.3 ECO. The 0.7 ECO (red line) has to be above its trigger line (yellow line) to go long. I marked the filtered trades with blue arrows, and marked a potential early trade (with no 0.7 ECO confirmation) in magenta:

ES 12-09 9_23_2009 (PnF 3 Ticks)

Download Links

The first one is available for ninjatrader, eSignal, multicharts, and Tradestation. If anyone converts it to their favorite platform, I’ll be happy to post it here with credit to the author.

Be sure to check the free-stuff tag for all posts giving away stuff for free.

Comments

  • SamG
    Hello Richard,

    What is the technical difference between the crossover of the ECO ( which happens earlier) versus when the ECO crosses the zero line ( which happens subsequently). What is the risk of going with the first crossover versus the "safe" entry which is when the ECO crosses 0?
    I just want to have a better understanding on how to use it effectively and trying to balance the desire for an early entry vs the higher risk that is involved in the crossover...

    Thanks in advance....
    SamG
  • RichardTodd
    Like a MACD or any similar indicator, it goes like this: When it crosses the 0 line, it has a new dominant direction over recent action. When it crosses the trigger line (histogram crosses 0), then the dominant direction is weakening. So, you have a knife and a hungy family. Are you going to attack the bear when it looks a little sick, or are you going to wait for it to keel over?
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