In Elliot wave theory the fourth wave is a correction before the final fifth wave in a trend. Wave 4s are characterised as being longer and more complex than the other waves in the cycle and can appear as triangles or complex ‘3s’, double or treble flats or double or treble zigzags.
There is quite a lot of information compared to other waves regarding their behaviour, their probable length and even methods for calculating the time it takes for them to unfold. In many ways they are more predictable than other waves. Take, for example, this quote in the book the Elliot Wave Principle considered by many to be the Elliotician’s ‘bible’:
“Fourth waves are predictable in both depth and form, because by alternation they should differ from the previous second wave of the same degree.”
On the page 66 there is this further unique and thrilling sentence:
“No market approach other than the Wave Principle gives a satisfactory answer to the question, “How far down can a bear market be expected to go?” The primary guideline is that corrections, especially when they themselves are fourth waves, tend to register their maximum retracement within the span of travel of the previous fourth wave of one lesser degree, most commonly near the level of its terminus.” (My italics).
No other theory purports to predict price movements so accurately. Armed with this technique the analyst can forecast the end of a correction and the resumption of the trend with ease – with incredible ease in fact. And yet the question ultimately has to be – does the guideline actually work? In this article I set out to see whether it does and also to test some other commonly held beliefs about the behaviour of fourth waves.
One of the difficulties in testing Elliot Wave theory it is that there is no standard agreement on how market activity should be labelled. This means that where one analysts sees an impulse wave another might interpret a zigzag. It is common for there to be two or more possible ways of labelling market activity in to wave patterns. This poses an experimental problem since it makes it impossible to definitively test data. Whether a wave is a wave 4 or another wave is itself the subject of hotly contested debate so how can we set up an experiment to usefully test how wave 4’s behave?
There is no absolute way of getting around this problem but there is a way of simplifying the process of identifying waves and reducing the number of different possible interpretations. The Elliot Wave Oscillator (EWO) is an indicator which can be used to distinguish waves in market activity and gives results which are largely unambiguous. The use of this aid in classifying market behavior therefore offers a certain level of ‘objectivity’. Whilst it is true that the use of the EWO can throw up wave configurations which are not easily assimilated into Elliot theory and break some of the rules of construction (as I have explored in another paper) it is a more objective approach than simply counting waves by eye.
How the Elliot Wave Oscillator works
The EWO is a MACD indicator on a 5,34,5 setting. It is generally used on a specific size of wave which is composed of between 100 and 140 price bars. The oscillator signals waves as follows:
a)Wave 3 is signalled as near completion when MACD has made an extreme peak or trough.
b)Wave 4 is signalled as near completion when the MACD moves back over the zero-line after the extreme peak or trough which signalled 3.
c) Wave 5 is in progress when the MACD re-crosses the zero-line, and finishes when the MACD makes a smaller hump to that made by wave 3 – and when there is divergence or convergence with price and MACD.
The diagram below illustrates the use of the Elliot Wave Oscillator in identifying waves.
Using the EWO, wave 4 becomes a more easily ‘objectifiable’ and measurable entity. It begins after the peak of the MACD oscillator when price reaches an extreme at the end of wave 3; and it ends when the counter-trend rally reaches a peak and the MACD has crossed the zero-line.
Using this method of isolating wave 4s I set out to measure their length and breadth and test certain core beliefs and assumptions in Elliot wave theory. I stuck to the 100 – 140 bar criteria for the EWO. A total of 52 waves were studied, on intraday charts ranging from 30 minute to 1 minute time-frames. The period studied was between June and October 2010. The waves were studied in sequence. An excel spreadsheet with details of each wave studied is attached.
Wave 4 never moves beyond the end of wave 1..
This is a fundamental rule of Elliot Wave construction: wave 4 must never move beyond the end of wave 1 – unless the construction is a rare diagonal formation in which wave 4 is allowed to move back into the territory of wave 1. The research data seemed to verify this basic tenet of the wave theory with only 3 out of the 52 waves exhibiting wave 4s which entered the territory of wave 1.
Back to the previous wave of lesser degree
This is the guideline stated in the opening paragraph, which appears in Prechter and Frost’s book the Elliot Wave Principle. Basically it states that wave 4 corrections tend to end in the territory of the wave 4 of lesser degree, most usually at its terminus.
The results showed that although the guideline was useful in a substantial number of cases it did not apply to all cases, and the majority of wave 4s actually corrected back further than the wave 4 of lesser degree, well into the territory of wave 3. The pie chart below should clarify the results:
Whilst it was not possible to be absolutely sure where the wave 4 of lesser degree began and ended – and this was a necessarily interpretative exercise – I tried to look at the charts as if analysing them in real-time using the EWO where applicable on smaller timeframes or a dash of ‘common sense’.
Interestingly, of the waves which corrected further the largest group ended in the centre of wave 3, at the midpoint.
A note on the data below: 6 of the 7 waves which ended in a consolidation in wave 3 also ended at the midpoint of wave 3.
It was observed that there is often a ‘kink’ at the midpoint of wave 3, that is a very small consolidation almost exactly at its midpoint. It was often the case that wave 4 retraced to this point and stopped there before reversing. This ‘kink’ phenomenon is shown in the diagram below:
The Fibonacci method for forecasting the length in time of wave 4s
There are not only methods for measuring the depth of retracement of wave 4s but also methods for measuring the length of time they take to unfold. One method advocated is the Fibonacci time method which involves taking the length of time in bars from the end of wave 1 to the end of wave 3 and multiplying the result by 1.38 and 1.62. These 2 results are then added to the end of wave 2 and extrapolated into the future to determine where the end of wave 4 will occur. The majority of wave 4s should end in the zone between the two lengths. This method is the one proposed in the book Trading Chaos by Dr. Bill Williams:
“You will find that most wave 4s will end in the time period between 1.38 and 1.62 times the length from the peak of wave 1 to the peak of wave 3 when measured from the bottom of wave 2.” p128.
When tested on real data the results showed that actually most wave 4s did not end in the zone suggested above. The pie chart below gives a breakdown of where the real wave 4 endings occurred.
The data above shows that the vast majority of wave 4s in the study were actually shorter than asserted by the method.
Although the sample size was rather small and more research is required to verify it, there also seemed to be a cyclical effect on the length of wave 4s. After analysing the difference between wave 4s in impulses in the same direction as the larger trend and those against the direction of the larger trend there was a significant difference between those which went beyond the 1.618 mark. Extra long wave 4s were more common in corrective impulses than trending impulses.
This was perhaps not surprising, given the strong counter cyclical forces at work which could help lengthen the wave 4 when it occurred in a corrective impulse. This might imply that Elliot waves in their length are influenced by larger cycles – a notion already put forward by several writers on the subject already.
Alternation describes how corrective waves behave differently from those that precede them in the unfolding of an Elliot cycle and how they tend to take a form which is the mirror opposite to the corrective wave which preceded them. This means that a particularly short corrective wave might be followed by a particularly long corrective wave or a simple 2nd wave by a complex 4th wave.
The results show that in fact the majority of the waves analysed did show some degree of alternation although a substantial number – 12 of the 52 did not show any obvious signs of alternation. The most common form was for the 2nd wave to be small and short and the 4th to be long and large. The second most common was alternation between acute wave 2s and shallow wave 4s.
Wave size as a Factor
A further part of the study focused on whether wave size was a factor in determining results. To this end the impulse waves in the study were broken down into 3 sub-groupings – comprised of those over 1000mins in length, those between 500 and 1000mins and those below 500mins. They were then analysed to see if there was any difference in their results.
Below are the results for the study for the depth of the 4th wave. Broadly there appeared to be no obvious differences between the results in the different sub-sets, although the larger waves had a higher proportion of shallow wave 4s then the smaller waves. Nevertheless a larger sample would be required to confirm this.
The aim of this study was to test commonly held assumptions about the behaviour of fourth waves. In as far as it was possible to be objective this was attempted with the aid of the EWO. The results showed that there was some validity in the guideline that wave 4s usually end in the territory of the wave 4 of lesser degree but that the majority actually probably went further, ending up to or near the midpoint of wave 3. The results moreover completely disagreed with the: “most commonly near the level of its terminus.” Second clause of the guideline, as only a handful ended at the terminus.
The proposition that most wave 4’s end in a Fibonacci generated zone between 1.38 and 1.62 times the length of time from the end of wave 1 to the end of wave 3 added to the end of wave 2 failed to hold when tested against the results from the study. In fact the largest number of the wave 4s ended before the zone and were shorter in time.
The presence of alternation was verified by the results but its application was limited given most alternation is between small 2s and large 4s or acute 2s and shallow 4s, nevertheless the principle worked in most cases.
Waves of different sizes were also studied as separate sets and it was found that no substantial difference existed between them, other than a possible relationship with depth which might be shallower in larger waves, although the data was insufficient to prove this and a larger number of observations in each of the subsets would be required for verification.