ELLIOTT WAVE FRACTALS

One of the basic tenets of Elliott Wave theory is that market structure is fractal in character. The non-scientific explanation of this fractal character is that Elliott Wave patterns that show up on long term charts are identical to, and will also show up on short term charts, albeit with sometimes more complex structures. This property of fractals is called "self-similarity" or "self-affinity" and it is what this writer is referring to when he says that the market is fractal in character.

The February, 1999 issue of Scientific American presents a cover article by the well-known scientist Benoit Mandelbrot. In "A Fractal Walk Down Wall Street," Mandelbrot claims to have discovered self-affinity in markets, i.e., the idea that fluctuations at small scales are no different from those at large scales. Robert Prechter took Benoit Mandelbrot to task for taking credit for the work RN Elliott did in the 1930s.

COUNTING FRACTALS

Our use of the word fractal, or Elliott Wave fractal, is not a proper use of the property of self-similarity. When we use the term here we mean a "counting fractal," which is really a description of the relative position of a bar on a high-low bar chart. This may create confusion but we do not want to hijack 'Elliott Wave Fractal' from Dr. Bill Williams, the originator of the expression.

Using so called fractals to count Elliott Waves first appeared, to our knowledge, in Dr. Bill Williams' book "Trading Chaos." Like many other concepts in Dr. Willams' books, the fractal is elegant in its simplicity. The basic definition of an 'up' fractal is a bar high that is both higher than the two bars immediately preceding it, and higher than the two bars immediately following it. The lows of the bars are not considered in determining the up fractal progression.

If two bars in the progression have equal highs followed by two consecutive bars with lower highs, then a total of six bars rather than the usual five bars will make up the progression. The first high becomes the counting fractal. Reverse for 'down' fractals.

A wide range bar can be both an 'up' fractal and a 'down' fractal at the same time.

FRACTAL WAVE COUNTING IS A BREAKTHROUGH

Using fractals to count Elliott Waves is a breakthrough because any particular bar either is a fractal or it is not a fractal. There are no half-pregnant fractals. You will especially appreciate this if you have ever tried counting waves from a close only line chart.

HOW TO DEAL WITH FUGITIVE FRACTALS

In a perfect world every time frame chart would have unambiguous sequences of up and down fractals to mark every Elliott Wave. Unfortunately, that's not the case. Quite often the fractal progression is broken with what we call 'fugitive' fractals', for example, two clearly marked up fractals with no intervening down fractal to unambiguously complete the wave. In these cases you have to use your own judgment and go lower or higher in time frames, or use a close only chart to resolve the relative importance of the fugitive fractal and whether or not it should be "forced" into the wave count.

Fractals always mark the beginning and ending points of individual waves. As Dr. Williams put it, "Whatever happens between fractals is an Elliott Wave."

FRACTALS ARE BEST COMBINED WITH THE ELLIOTT OSCILLATOR

Counting fractals can be combined with the Elliott Wave Oscillator to get as close to unambiguous wave counts as Elliott Wave theory allows. Here's an example of fractal counting . And yes, you would lose the debate with Robert Prechter on the purity of Momentum Waves as an integral part of Elliott Wave theory.

The 5 bar formation works best on Daily or longer time frame charts. For intraday data charts we often use 9 bar, 13 bar and 21 bar formations for fractal counting.

The Investor/RT Fractal indicator is based upon the "Bill Williams Fractal" in the book "Trading Chaos" by Bill Williams, PhD.  A fractal is an entry technique that is traditionally defined as "a bar that has two preceding and two following bars with lower highs (or lower lows, on a down move)".  Several different varieties of up and down bar 5-bar fractal formations can be seen below.

THE ELLIOTT OSCILLATOR

The Elliott Oscillator, or 5/34 Oscillator, is a 34 period simple moving average of prices subtracted from a 5 period simple moving average of prices displayed as a histogram above and below a zero line. You can duplicate the Elliott Oscillator on charting programs with a MACD feature. It can be applied to any time frame (intraday, daily, etc.) and works equally as well in every time frame provided that the correct number of bars are displayed in the chart. The chart below is a good example of how effective this technique can be in counting Momentum Waves.

Whether or not Momentum Waves could be considered as true Elliott Waves is not important. We just accept that they are not and use them for what they are very good at doing, identifying the current state and the probable termination point of a swing. The most important single concept about the Elliott Oscillator is that the highest/lowest point of the Oscillator is connected to the bullish/bearish Wave 3 of the swing.  Related concepts are that Wave 4 crosses the zero line in the opposite direction of the trend. Wave 5 often makes a new high or low price for the swing but always diverges from the Oscillator. If the suspected Wave 5 makes a new extreme price simultaneously with a new Oscillator extreme then it is not a Wave 5. This happens fairly often with intraday charts. What you're seeing in that situation is an extended Third Wave which carries the implication of a significant price move in the direction of the trend yet to come.

OPERATIVE TIME FRAME CHARTS

The Elliott Oscillator is most effective when the chart has the "correct" number of bars. From 100 to 150 bars is the correct number of bars to use with the oscillator. Dr. Bill Williams suggests 100-140. Tom Joseph implies that 150 is right. We like to use about 120 bars, which is comfortably in the middle of that range, and which has consistently produced reliable results.

There is nothing magic about 120 days, 120 hours or 120 minutes. Although an Operative Time Frame Chart could coincidentally be any of these time periods, constructing this chart has nothing to do with fixed time periods. Put simply, an Operative Time Frame Chart is a bar chart that starts at a significant pivot point and displays 120 bars of the swing that started at that particular pivot point. If analyzing small time frames, like on our Hourly Charts, an Operative Time Frame chart will display about 120 bars of anywhere from 15 to 240 minutes of intraday data. The time period of the bars in the chart is arranged to always show the swing as an event consisting of about 120 bars. The sample SPX chart comprises 85 minute bars. This more recent Eurodollar chart comprises two day bars. The completed five wave sequence would be invalidated by any move below the suspected 5th wave 1.17 low.

WHAT CAN YOU DO WITH AN OPERATIVE TIME FRAME CHART?

• Closely determine the probable time period of the end of a correction.
• Avoid losses by reversing too early on a swing that looks complete.
• Closely determine the likely termination of a swing of any degree.
• Decide in one second whether you should be long or short.

Not bad credentials for a simple tool.