An Investigation of the Elliott Wave Oscillator

In the heavy chop of market action, it can be difficult to make head or tail of the trend. Let alone come up with an acceptable Elliott Wave count. One tool often used as an aid to help the analyst is the Elliott Wave Oscillator (EWO). This article explores the use of this new tool and draws on original research to test its value. In the end, it posits new insights into the underlying structure of the market and questions some of the ideas and assumptions put forward by leading market thinkers and analysts in their work.

Elliot Wave Oscillator

The EWO signals the end of waves: the end of wave three is signalled when the MACD reaches its highest point – its peak; the end of wave four is signalled when the MACD comes back down to below the zero-line and the end of 5 when the MACD rises back up over the zero-line and makes a lower MACD peak, thus setting up a bearish divergence with a price – assuming that is wave five is not ‘truncated’ of course.

100 – 140 bars

In his book, ‘Trading Chaos’ trading coach Bill Williams describes a further refinement of the EWO in which he advocates analyzing waves using only a specific period of between 100 and 140 price bars. He says research has led him to find that this is the optimum timeframe for analyzing a complete Elliott wave using the EWO. In this research, this enhancement has been incorporated as a rule, except in exceptional situations when it was impossible to fit market action into 100-140 bars because of the limitations of the software used.

The Research Data

Two periods were analyzed, from August 6th to October 20th 2010 and also a smaller period in June 2010. All in all, 100 ‘waves’ were analyzed between 1 minute and 30-minute airframes. A list of all the waves with all their data is included in a spreadsheet on a separate document.

Initial Observations

Not all the waves observed in the sequence were impulses containing the constituent waves and diverging MACD tops so easily identifiable using the EWO pictured at the start of this article. The second category of patterns emerged, which had the important distinction of not having diverging MACD peaks. Because of their shape and prevalence in corrective and sideways markets, they were annotated as ‘zig-zag’ and categorized differently. These non-diverging patterns were quite common, making up 40 of the 100 waves. 5% of waves also fitted into a further 3rd category named ‘Triangles’. These were really consolidation zones which were too messy and small to unravel and analyze, so they were cordoned off and treated separately.

The three main types of market patterns:

1. Impulses (55%)


2. Zig-zags (40%)


3. Triangles (5%)


Waves within waves forever.

In Trading Chaos Williams makes the point that the market is made up of a basic waveform – the Elliott wave – and that this wave recurs over and over again.

“The Elliott sequence consists of a basic rhythm of ‘fives’ corrected by ‘threes’. This sequence remains constant no matter what degree of the wave is being analyzed.”

The same point is made by Robert Prechter in Elliott Wave Principle. It is the argument that the Elliott Wave is the basic building block of the market and that it recurs as waves within waves over and over ad infinitum.

It was discovered that at a certain point, it was not possible to break market segments down to into their smaller constituent elements due to limitations in the charting package.

Further, research using the EWO found market action did not always follow the rules and prescriptions of Elliot’s theory. Whilst it was true that most of the time impulse waves were found in the direction of the main trend and zig-zags as corrections of the trend, there were also many cases where zig-zags were found as parts of the trend (i.e. in the place of impulses), and impulses were found as corrections. There were also examples of several impulses following each other with no zig-zag break in-between. This was too common an occurrence to be ignored and raised question marks as to the validity of the theory.

Mixing Form and Function

One of the basic tenets of Elliott Wave theory is that impulses tend to be five wave affairs and corrections three waves. However, this research found that in reality, this is only partly true.

To illustrate this, take waves 82, 83 and 84 (see pic below). These three waves could be analyzed as discreet entities in themselves at a lower degree or as a whole impulse. As discreet entities, they would be labelled as follows: zig-zag – zig-zag – impulse because 82 and 83 are non-diverging patterns followed by 84, which is a diverging pattern. However, zooming out a degree the three condensed together as a whole are a fine example of a classic impulse.

Mixing Form and Function

Because the three waves above were analyzed as the market unfolded and not with the benefit of hindsight, they were analyzed discreetly as smaller segments first. It was only later that it was discovered they were a part of a larger wave as price activity unravelled down the line. However, by this fortuitous accident of chance, the researcher gained an insight into how difficult it can be to use the EWO in real-time as well as gaining an understanding of the elements hidden within waves.

That the larger wave turned out to be an impulse in the direction of the main trend questioned the already existing assumption that impulses are made up of smaller impulses and zig-zags occur as corrections. Therefore, whether because of shortcomings of the Elliott wave theory itself or because of the failure of the EWO the original rules of construction did not always apply thus raising doubts about the efficacy of the ‘Russian Dolls‘ element to Elliott theory.

Impulses Masquerading as Corrections

Another aberration from classical theory was the observation during the research that impulses could sometimes begin corrective phases – particularly rolling down off the highs, such as in the example of waves 47 – 49 (see pic below). This inexplicable occurrence – of impulse waves within a correction of the larger trend could not even be explained by identifying them as the initial wave of a larger scale zig-zag, because at a higher degree the two impulses just turned out to form a larger impulse instead. Therefore even at a higher degree, the EWO failed to distinguish between corrective and impulsive patterns as set down in orthodox Elliott theory.

This ambiguity could easily fool a trader into believing a major reversal from bull to bear had occurred because the trader might witness the first five waves down and believe this to be the start of a whole new bear market phase when it was itself the total of a correction. Another example of the phenomenon of corrective sequences wrongly diagnosed as impulses by EWO occurred at the large corrective wave 19.


Fitting wave counts into larger wave patterns.

It was difficult to fit the small waves analyzed by the EWO in this research into larger wave patterns and confidently build up satisfying higher degree wave counts. However, this may have been partly due to the insufficient size of the sample. As noted above, one of the problems was that corrections could wrongly be identified as reversals. Still, another problem was the ability of impulses to seemingly endlessly unravel one after another with no ‘end in sight’.

Waves 35 – 60 are all a part of a one larger degree wave, and it could be difficult to predict when the final 5th of the 5th was going to occur if the analysis had been done in real-time. The best explanation, in this case, is that the larger degree wave was an extension, but this recourse to exceptions highlights one of the Elliotician’s most common faults, which is to call the last wave of a move prematurely. Indeed probably the most notable Elliotician of all, Robert Prechter made this mistake himself in the 90’s when he called a top in the DOW only to see it rise much further in an extended 5th wave, which constituted the dot-com bubble.

Technical applications

Whilst the EWO only had marginal value in building Elliott counts, it did have a useful short term application as a means for categorizing two distinct types of market behaviour – the diverging from non-diverging – or impulses from zig-zags. These results seem to point to a perhaps more chaotic, more complex but truer picture of the market than the neat and tidy world of Elliott Waves promises.

Impulses & Zig-Zags

The research found that the majority of market action observed was made up of diverging and non-diverging patterns or in other words, impulses and zig-zags. Of the 100 waves studied 55 were impulses, 40 zig-zags and five were triangular. The corrective patterns did not always follow the impulses in an alternating fashion as would be expected from classic Elliott theory but rather tended to cluster if anything, particularly the zig-zags which clustered between waves 43 – 48 and 78 – 84.

One thing which did back up existing theory was that impulses tended to be more commonly found in the ‘trend’ of a degree higher with 27 of the 36 trending patterns impulses. Impulses were also quite common in corrective activity as well, however, with 25 of the 50 corrective patterns being impulses and only 20 being zig-zags (the other five triangles). This was the most surprising statistic since it went against commonly held Elliott theory.

Rate-of-Change (ROC)

There was quite a large difference noted between the average ROC for the two classes of patterns. While impulses tended to be part of the main trend more frequently than zig-zags, their average ROC was lower at 2.460 pips/minute (ppm) compared to 5.666 ppm for zig-zags and which, even if the one massive outlier was removed (which had a ROC of 83.333ppm) gave a score of 3.622 ppm, still almost 50% higher than the average for impulses. However, it ought to be noted that it was observed that commonly waves of shorter lengths tended to score higher on ROC than longer waves and given zig-zags tended to be shorter, their ROC readings were bound to be higher on average.


Zig Zag ROC

ROC for 1000

Looking at the scatter distribution charts above of the ROCs for the two pattern types and the 1000 pip plus wave ROC chart, we see that the main difference between the two patterns is the increased density of the clustering in the impulse chart beneath 4ppms, whereas the zig-zags show less consistency, although many of them are also beneath the 4ppms figure (outlier again removed). The final chart shows how longer waves tend to smooth ROC to a lower level – and given most longer waves were impulses, this explains their lower average ROC.

The exact number below four pips per minute is 26 (66%) for zig-zags and 46 (84%) for impulses. Conclusion: a higher rock reading may well be a defining characteristic for distinguishing between the two patterns. The vast number of impulses have ROC of below four pips per minute.

Pattern length and time

Zig-zags had an average time period of 499 minutes whilst impulses had an average length of 1100 minutes. This would seem to make sense given divergence requires time and so impulses would be expected to exhibit a greater time-span.

Length of C waves and 5th waves

Compared to 5th waves in impulses, zig-zags had longer C waves. 17 out of the 24 waves with the longest terminal waves (in relation to the whole) were zig-zags. Longest was defined as being 75% or longer than the total length of the entire movie.

The averages for the different pattern types showed that impulse 5th waves averaged 50% the length of the entire movie, whilst zig-zags on average exhibited much longer terminal waves, at an average of 74.87% of the length of the total move. Only 6 out of the 55 impulse waves had truncated 5th waves.

As can be seen from the graph below, which shows the number of pips by which 5th waves surpassed 3rd wave peaks and also the pips that C waves surpassed their wave A peaks, most wave 5’s surpassed the peaks of wave 3’s by up to 300 pips, with the majority falling in the 0 – 220 band.

The end of 5

With zig-zags, there were no truncated C waves – all of them surpassed the peak of the wave.


The end of C

There was quite a wide distribution in zig-zags although few beyond 700 pips and a cluster around the 500 pip mark.

Length of B waves and 4th waves and percentage retracements

90% of all wave four or B wave retracements ended in the region of somewhere between 20% and 80% of the previous move as illustrated below.

Wave 4B

Overall impulses exhibited shallower retracements compared to zig-zags with 80%, or 44 of the 55 impulses, showing wave four retracements of less than 60%.

Wave 4

Only 22 of the 40 zig-zags exhibited B waves which retraced less than 60% of the previous move. This works out as 55% – as compared to 80% for impulses. There was a much wider variation in the amount B waves retraced A waves, as can be seen by the highly scattered effect on the graph below.

Wave B

Assessing the ‘Target zone’ – the end of wave 5

Finally, another of the tools used by Dr Bill Williams in Trading Chaos could be tested, namely the method for finding the end of wave five which he attributes to another analyst/trader called Tom Joseph. The ‘Tragetzone’ for five is found by taking the length of waves 1-3 and extrapolating that figure by 61.8% -100%, and then adding that to the low of wave 4.

The results of the research found that the average length of 5 in relation to 1-3 was 60.17% – which is close enough, although a little low perhaps. The distribution chart below shows all the lengths of the wave 5’s researched in percentage terms from the impulses studied – please ignore the minus scale. It shows quite a wide distribution and seems to disprove William’s method. It appears that far from the vast majority of wave 5’s ending in the ‘target zone’ between 61.8% and 100% only 26 out of the 55 impulses, which is 47.27%, actually went further than 61.8% at all and five overshot 100% so it is debatable whether they should strictly speaking be included. If you remove these then only 21 conform to the guideline exactly – that is 38.2% of all the impulses.

Actually, the research shows most wave 5s ended in a target zone between 26% and 84% of the extrapolation of 1-3 from 4. This wider band included 81.8% of all the wave 5s studied.

Wave 5

Zig-zag leg equality investigated.

It has always been accepted that zig-zags tend to exhibit equality in the lengths of legs A and C. This commonly held piece of market lore was tested. If indeed most zig-zags exhibited A and C leg equality, then this should be borne out by the results.

However, the results showed that the overall average length of C compared to A was 134.31% – higher than the 100% for equality. On average wave C was longer than wave A. The graph below shows the distribution of lengths; again please ignore the minus scale.

Wave C1

Taking out the two outlier results near the 500% mark, we can see the distribution in more detail. It shows that the vast majority of C waves in the research were between 60% and 200% the length of wave A.

Wave C2

It is clear that whilst plenty of wave C’s were close to equality or 100% of A; there was a sizeable number which was longer too.

A note on Triangles

The sample of 5 triangles was too small to undertake any worthy analysis, suffice to say they more or less followed Elliot’s rules except in relation to their position in the market as was the case with the other observable patterns.

Conclusion and Further Research

The EWO was an insufficient tool for removing the ambiguity from Elliott Wave analysis and coming up with more reliable wave counts – although a larger segment of the market probably needs to be analyzed to be certain of this. The research suggests that the method outline in Dr Bill William’s book Trading Chaos to pinpoint the end of wave five may be inaccurate too.

The research defined three important constituents ‘modes’ of market behaviour observable through the ‘lens’ of the Elliott Wave Oscillator viz diverging, non-diverging and triangular, and that these occur in a random or clustering fashion not alternate as the Elliott theory suggests. Based on the use of the EWO, it appears that these would be better described as the basic building blocks of the market more than the simple 5-3 Elliott wave.

Further research would focus on adding definition to the three modes of behaviour and attempting to identify ways in which market practitioners could identify them at earlier stages of their development thus enabling them to take advantage of their potential as tradable patterns. Indeed the work begun on the lengths of individual pattern waves could become an invaluable source for assessing risk and finding optimal entry and exit positions in real-time during trading.

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1 thought on “An Investigation of the Elliott Wave Oscillator”

  1. Great detail about Elliott Wave Oscillator. Here you almost cover everything about Elliott Wave. Thanks for sharing this kind of helpful tutorial.


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