finally beenfalsified and it was time for a new one. In 1921, Albert Einstein respondedproperly by putting forward his new and more informative Theory of Gen-eral Relativity. Today, almost one hundred years later, Einstein’s theoryhas survived all attempts to falsify it.
Newton's theory qualified as scientific because it was open to empiri-cal refutation. In fact, Newton's theory was not wrong so much as it wasincomplete. Einstein’s General Theory of Relativity not only accounted forall of the phenomena covered by the Newtonian model, but it accommo-dated the new observations that conflicted with Newton’s more limitedtheory. This is how science progresses. Longevity and seniority meannothing. Predictive accuracy and explanatory power are everything.
The case of Adams and Leverier make clear why claims must be opento empirical refutation. Falsifiability alone gives scientific knowledge alarge advantage over conventional wisdom. The ability to jettison false orincomplete ideas and replace them with ever more informative ones pro-duces a body of knowledge that is self-correcting and in a continual stateof improvement. This in turn provides a stable base upon which new ideascan be erected that reach ever higher levels of understanding. Intellectualactivities that have no procedure for eliminating erroneous knowledge in-evitably get bogged down in nonsense. This is precisely the problem withthe popular version of TA.
Now we will consider an example of an improper response to falsi-fication. It occurs in the field of finance. The injection of science into fi-nance is relatively recent. Perhaps this explains the defensive,unscientific response of those who support the efficient markets hy-pothesis. When observations collided with their favorite theory, theytried to save it from falsification by reducing its information content. Asmentioned earlier, its least informative version, EMH weak, predicts842 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
that investment strategies based on TA” will not be able to earn risk ad-justed returns that beat the market index. When EMH supporters werefaced with studies showing that TA-based strategies were able to earnexcess returns,” they responded by trying to immunize their theoryfrom falsification. They did so by inventing new risk factors andclaimed that the excess returns earned by TA were merely compensa-tion for risks inherent in pursuing such a strategy. In other words, EMHdefenders claimed that investors who followed the TA strategy were ex-posing themselves to a risk that was specific to that strategy. This al-lowed the EMH supporter to characterize the TA strategy’s returns asnon-market-beating. Recall EMH does not claim that earning returnshigher than the market is impossible. It only says that higher returns en-tail the assumption of additional risk. If the returns earned by the TAstrategy were indeed compensation for bearing higher risk, then EMHwould remain intact despite the studies that show TA strategy earning areturn higher than the market index.
There was one problem with the way EMH supporters did this. Theycooked up the risk factor after the TA studies had been performed." Thisis not kosher science. It would have been scientifically correct if EMHhad defined the risk factor in advance of the study and predicted that atest of the TA method would generate what appeared to be market-beatingreturns. Had they done this, the status of EMH would have been en-hanced with a successful prediction. Instead, EMH supporters took thelow road to save their favored hypothesis by giving themselves the li-cense to invent a new risk factor any time they needed to explain awayfindings that conflicted with their favored theory. In so doing, EMH sup-porters rendered their hypothesis unfalsifiable, thereby draining it of anyinformation content.
The precedent for this knowledge-regressive method of immunizingthe EMH hypothesis against falsification had already been establishedby earlier flawed defenses of EMH. These earlier, and similarly misguided,efforts to save EMH were in response to studies that had shown thatpublic fundamental information, such as the price-to-book ratio and PEratio, could be used to generate excess returns.”° In response to this in-convenient evidence, EMH defenders claimed that low price-to-book ra-tios and low PE ratios were merely signals of stocks with abnormallyhigh risk. In other words, the fact that a stock’s price is low relative toits book value is an indication that the company is facing difficulties. Ofcourse, this reasoning is circular. What is key here is the fact that EMHadvocates had not defined low price-to-book or low PE as risk factors inadvance of the studies showing that stocks with these traits were able toearn excess returns. Had EMH theorists done so, it they would have bol-The Scientific Method and Technical Analysis 143
stered the information content of EMH with an additional dimension ofrisk. Instead, EMH theorists invented these risk factors after the fact, forthe specific purpose of explaining away discordant observations thathad already been made. Such explanations are termed ad-hoc hypothe-ses—explanations invented after the fact for the specific purpose of sav-ing a theory or hypothesis from being falsified. Popper referred to thisknowledge regressive, save-the-theory-at-any-cost behavior as falsifica-tion immunization.
Had Popper known of it, he would have chastised the die-hard sup-porters of EMH, but he would have probably applauded the efforts ofthose advocating behavioral finance. This relatively new field has pro-posed testable hypotheses that explain the profitability of strategies basedon public technical and fundamental data as arising from the cognitive bi-ases and illusions of investors. It is ironic that erroneous beliefs in the va-lidity of subjective TA and the valid profitability of some forms ofobjective TA may both be the result of cognitive foibles.
The Scientific Attitude: Open yet Skeptical
Falsificationism makes a clear distinction between two phases of scien-tific discovery: proposal and refutation. These phases demand differentmindsets—openness and skepticism. The coexistence of these oppositemindsets defines the scientific attitude.
An attitude of openness to new ideas is vital when hypotheses arebeing formulated. The willingness*® to see things in a new way, to ad-vance new explanations and take bold inductive leaps characterizes theproposal phase. Most practitioners of TA function well in this mode.New indicators, new systems, and new patterns get proposed all thetime.
However, once a bold conjecture has been made, receptivity mustmorph into skepticism. Doubt about the new idea motivates a relentlesssearch for its flaws. Thus, there is an ongoing tension in the scientist’smind between speculative curiosity and hard-nosed disbelief. However,the doubt is not an unremitting skepticism but one that yields to persua-sive new evidence. This is the quasi-schizoid state that defines the scien-tific attitude.
Beyond the distrust of the new hypothesis, another form of skep-ticism thrives in the mind of a scientist: doubt about the mind itself.This springs from a profound awareness of the all-too-human tendencyto generalize hastily and leap to unfounded conclusions (see Chapter2). The procedures of science can be seen as safeguards against thesetendencies.9144 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
THE END RESULT:THE HYPOTHETICO-DEDUCTIVE METHOD
 
Some would say there is no such thing as the scientific method.” “The sci-entific method, as far as it is a method is nothing more than doing one’sdamnedest with one’s mind no holds barred.”** At its essence it is intelli-gent problem solving.
The problem-solving method used in science today has come to beknown as the hypothetico-deductive method. It is commonly described ashaving five stages: observation, hypothesis, prediction, verification, andconclusion. “In actual scientific work these stages are so intertwined thatit would be hard to fit the history of any scientific investigation into thisrigid scheme. Sometimes the different stages are merged or blurred, andfrequently they do not occur in the sequence listed.” Rather, it is a usefulway to think about the process.
The hypothetico-deductive method was initiated by Newton in theseventeenth century, but was not formally named until after Popper’s con-tributions were introduced. It is the outgrowth of several hundred years oftussling between scientists and philosophers. The method integrates bothinductive and deductive logic, paying heed to their individual limits whileleveraging their respective powers.
The Five Stages
1. Observation: A possible pattern or relationship is noticed in a set ofprior observations.
2. Hypothesis: Based on a mysterious mixture of insight, prior knowl-edge, and inductive generalization, it is hypothesized that the patternis not an artifact of the particular set of observations but one thatshould be found in any similar set of observations. The hypothesismay merely assert that the pattern is real (scientific law) or it may gofurther and offer an explanation about why the pattern exists (scien-tific theory).
3. Prediction: A prediction is deduced from the hypothesis and embod-ied in a conditional proposition. The proposition’s antecedent clauseis the hypothesis and its consequent clause is the prediction. The pre-diction tells us what should be observed in a new set of observationsif the hypothesis is indeed true. For example: If the hypothesis is true,then X should be observed if operation O is performed. The set ofoutcomes defined by X makes clear which future observations wouldconfirm the prediction and, more importantly, which future observa-tions would be in conflict with it.The Scientific Method and Technical Analysis 145
4.
Verification: New observations are made in accordance with the op-erations specified and compared to the predictions. In some sciencesthe operation is a controlled experiment. In other sciences it is an ob-servational study.
Conclusion: An inference about the truth or falsity of the hypothesisis made based on the degree to which the observations conform to theprediction. This stage involves statistical inference methods such asconfidence intervals and hypothesis tests, which are described inChapters 4 and 5.
An Example from TA
The following is an example of the hypothetico-deductive method as itwould be applied to testing a new idea about technical analysis.
1.
Observation: It is noticed that when a stock market index, such asthe Dow Jones average or the S&P 500, rises above its 200-day movingaverage, it generally continues to appreciate over the next severalmonths (probabilistic generalization).
Hypothesis: On the basis of this observation, inductive generaliza-tion, and prior findings of technical analysis, we propose the follow-ing hypothesis: Upward penetrations of the 200-day moving averageby the DJIA will, on average, produce profitable long positions overthe next three months. I'll refer to this hypothesis as 200-H.
. Prediction: On the basis of the hypothesis, we predict that an obser-
vational investigation, or back test, will be profitable. The hypothesisand the prediction are turned into the following conditional statement:If 200-H is true, then the back test will be profitable. However this pre-diction creates a logical problem. Even if the back test is profitable itwill not be helpful in proving the truth of 200-H because, as previouslypointed out, while a profitable back test would be consistent with thetruth of 200-H, it cannot prove that 200-H is true. An attempt to do sowould commit the fallacy of affirming the consequent (see argument 1below). If, on the other hand, the back test turns out to be unprof-itable, it would be valid to conclude 200-H is false by the valid logicalform falsification of the consequent. See Argument 2 below.
Argument 1Premise 1: If 200-H is true, then a back test will be profitable.Premise 2: The back test was profitable.
Invalid Conclusion: Therefore, 200-H is true. (fallacy of affirmingthe consequent)146 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
Argument 2
Premise 1: [f 200-H is true, then a back test will be profitable.Premise 2: The back test was NOT profitable.
Valid Conclusion: Therefore, 200-H is false.
However, our objective is to prove the truth of 200-H. To get aroundthis logical problem, suppose we had formulated a null hypothesis atstage 2, specifically, Upward penetrations of a 200-day moving aver-age do not generate profits over the following three months. Let’s re-fer to this as Null-200. From this we can formulate the followingconditional proposition: If Null-200 is true, then a back-test willNOT be profitable. If the back test does turn out to be profitable, wecan validly argue that the null hypothesis has been falsified (falsifyingthe consequent). By the Law of the Excluded Middle, either 200-H istrue or Null-200 is true. There is no middle ground; there is no otherhypothesis possible. Thus by disproving the null we will have indi-rectly proven that 200-H is true. Thus we have the following condi-tional syllogism:
Premise 1: [f Null-200 is true, then the back test will be un-
profitable.
Premise 2: The back test was NOT unprofitable (i.e., it wasprofitable).
Valid Conclusion: Null-200 is false, therefore 200-H is true.
4. Verification: The proposed rule is back tested and its profitability isobserved.
5. Conclusion: Determining the meaning of the results is a matter ofstatistical inference, the topic treated over the next three chapters.
RIGOROUS AND CRITICAL ANALYSIS OFOBSERVED RESULTS
 
The fifth phase of the hypothetico-deductive method points to another im-portant difference between science and nonscience. In science, observedevidence is not taken at face value. In other words, the obvious implica-tion of the evidence may not be its true implication. The evidence must besubjected to rigorous analysis before a conclusion can be drawn from it.The evidence of choice in science is quantitative data, and the tool ofchoice for drawing conclusions is statistical inference.
An important scientific principle is the preference for simpler expla-The Scientific Method and Technical Analysis 147
nations (Okam’s Razor). As such, astounding hypotheses are given seriousconsideration only after more commonplace hypotheses have been re-jected. Sightings of a UFO are not immediately interpreted as evidence ofan alien visit. More mundane accounts such as ball lightning, weather bal-loons, or a new aircraft must first be discredited before an invasion fromouter space is taken seriously.
Thus a scientific attitude toward an extraordinarily profitable ruleback test would first consider and reject other explanations before enter-taining the possibility that a significant TA rule has been discovered. Thepossible explanations of good performance unrelated to a rule’s predictivepower are good luck due to sampling error (see Chapters 4 and 5) and sys-tematic error due to data-mining bias (see Chapter 6).
SUMMARY OF KEY ASPECTS OF THESCIENTIFIC METHOD
 
The following is a summary of the key points of the scientific method:
¢ No matter how voluminous the evidence, the scientific method cannever conclusively prove a hypothesis to be true.
¢ Observed evidence used in combination with the deductive form falsi-fication of the consequent can be used to disprove a hypothesis with aspecified degree of probability.
¢ Science is restricted to testable hypotheses. Propositions that are nottestable are not within the domain of scientific discourse and are con-sidered to be meaningless.
e A hypothesis is testable if and only if predictions about yet-to-be-made observations can be deduced from the hypothesis.
¢ A hypothesis that can only explain past observations but that cannotmake predictions about new observations is not scientific.
e Ahypothesis is tested by comparing its predictions with new observa-tions. If predictions and observations agree, the hypothesis is notproven, but merely receives tentative confirmation. If they don’tagree, the hypothesis is taken to be false or incomplete.
e All currently accepted scientific knowledge is only provisionally true.Its truth is temporary until a test shows it to be false, at which point itis replaced or subsumed by a more complete theory.
© Scientific knowledge is cumulative and progressive. As older hypothe-ses are shown to be false, they are replaced by newer ones that moreaccurately portray objective reality. Science is the only method of in-quiry or intellectual discipline which can claim that newer is better.148 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
Though knowledge, styles, and methods in other disciplines, such asmusic, art, philosophy, or literary criticism, may change over time, itcannot be claimed that new is necessarily better.
e Any set of past observations (data) can be explained by an infinitenumber of hypotheses. For example, Elliott Wave Theory, GannLines, classical chart patterns, and a roster of other interpretivemethods can all explain past market behavior according to theirown paradigm of analysis. Therefore, all these explanations aresaid to be empirically equal. The only way to decide which ones arebetter is by seeing how well they can predict observations whoseoutcomes are not yet known. Those methods that cannot generatetestable (falsifiable) predictions about new observations can beeliminated immediately on the grounds that they are scientificallymeaningless. Those methods that can generate predictions that arefound to conflict with future observations can be eliminated ongrounds that they have been falsified. Thus, only methods that canmake testable predictions that display genuine predictive power de-serve to be retained in the body of TA knowledge.
IF TA WERE TO ADOPT THE SCIENTIFIC METHOD
 
This section examines consequences of TA adopting the scientificmethod.
The Elimination of Subjective TA
The most important consequence of TA adopting the scientific methodwould be the elimination of subjective approaches. Because they are nottestable, subjective methods are shielded from empirical challenge. Thismakes them worse than wrong. They are meaningless propositions devoidof information. Their elimination would make TA an entirely objectivepractice.
Subjective TA would be eliminated in one of two ways: by transforma-tion into objective methods or abandonment. Perhaps Gann Lines, subjec-tive divergences, trend channels, and a host of subjective patterns andconcepts embody valid aspects of market behavior. In their present sub-jective form, however, we are denied this knowledge.
Transforming a subjective method into an objective version is not triv-ial. To illustrate a case where this has been done, I discuss an algorithmfor the automated diction of head and shoulder patterns and test results inthe section “Objectification of Subjective TA: An Example.”The Scientific Method and Technical Analysis 149
Elimination of Meaningless Forecasts
It is not practical to assume that all subjective practitioners will followmy call to objectify or close up shop. For those who continue to usesubjective approaches, there is an important step that can be taken tomake their output, if not their methodology, objective. Henceforth, theywould issue only falsifiable forecasts. This would at least make the in-formation they provide meaningful and informative. In this context, in-formative does not necessarily mean correct but rather that theforecasts have cognitive content that passes the discernable differencetest discussed in the Introduction. In other words, the forecast wouldconvey something of substance, the truth of which can be clearly deter-mined by subsequent market action. In other words, the forecast willmake explicit or clearly imply which outcomes would show it to bewrong. As stated previously, a forecast that does not make clear whatfuture events constitute prediction errors in essence says that any out-come can happen.
At the present time, most subjective forecasts, often referred to asmarket calls, are meaningless. In all likelihood, this is not obvious to ei-ther consumers or the analysts issuing the forecasts. First, consider aforecast that is clearly meaningless: “My indicators are now predicting themarket will either go up an infinite percentage, down 100 percent, orsomething in between.” On its face, the statement is unfalsifiable becausethere is no outcome that could possibly conflict with the prediction. Theonly good thing about the forecast is that its lack of meaning and lack offalsifiability are transparent. A more typical market call goes somethinglike this: “On the basis of my indicators [fill in one or more TA methods], Iam bullish.” This unfalsifiable statement is just as meaningless, but its lackof substance is not obvious. Though there is a prediction of a rise, the pre-diction leaves unclear when it might occur or under what circumstancesthe prediction would be wrong.
This bullish stance could have been made meaningful by clearly ex-cluding certain outcomes. For example, I expect the market to rise morethan 10 percent from current levels before it declines by more than 5percent from current levels. Any instance of a decline of greater than 5percent before a rise of 10 percent would be sufficient to classify the fore-cast as an error.
If you ever suspect that you are being fed a meaningless prediction,here are some good antidotes. Ask the following question: “How much ad-verse movement (opposite to the direction predicted) would have to oc-cur for you to admit this forecast is mistaken?” Or “What outcomes areprecluded by your prediction?” Or “When, and under what conditions, canthe forecast be evaluated, such as the passage of time, change in price (ad-150 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
verse or favorable), or a specific indicator development?” Reader, I warnyou not to do this if you are squeamish about watching people squirm.
Making subjective forecasts meaningful with an up-front statement ofwhen and how the forecast will be evaluated would eliminate the marketguru's after-the-fact wiggle room. Some ways of adding meaning to a sub-jective forecast include (1) defining a future point in time when the fore-cast will be evaluated, (2) defining the maximum degree of adversemovement that would be allowed without declaring the prediction wrong,and (3) predicting a specified magnitude of favorable movement prior to aspecified magnitude of unfavorable movement (X percent favorable be-fore Y percent unfavorable). Steps like these would allow a subjectivepractitioner to develop a track record of meaningful market calls. Mean-ingful track records can also result from specific transaction recommen-dations made in real time.
One limitation of this recommendation is that it would still leave un-clear what the profitable track record represents. This is because subjec-tive forecasts are derived in an undefined way, so even if a profitable trackrecord of meaningful predictions is built up over time, it cannot be knownthat they were the result of a consistent analysis procedure that can be re-peated in the future. In fact, it is likely that the method of analysis is notstable over time. Studies of expert subjective judgment indicate that ex-perts do not combine information in a consistent manner from one judg-ment to the next. “Intuitive judgments suffer from serious randominconsistencies due to fatigue, boredom, and all the factors that make ushuman.”° In other words, given the exact same pattern of market data atdifferent times, it is quite possible that a subjective analyst would not givethe same forecast."!
Paradigm Shift
Refashioning TA into an objective practice would be what Thomas Kuhncalls a paradigm shift. In his highly influential book, The Structure of Sci-entific Revolutions, Kuhn rejected Popper’s notion that science evolvesstrictly by falsification and conjecture. Instead, Kuhn saw the evolution ofa science as a sequence of paradigms, or world views. While a given para-digm is in place, practitioners indoctrinated in that point of view confinetheir activities to posing questions and hypotheses that are consistentwith and answerable within that view.
A large number of TA analysts have been indoctrinated with the non-scientific, intuitive analysis paradigm developed by TA pioneers like Dow,Gann, Shabacker, Elliott, Edwards and Magee, and so forth. They estab-lished the subjective research tradition and postulated the backgroundwisdom that is accepted as true and taught to aspiring practitioners. TheThe Scientific Method and Technical Analysis 151
certification exam given by the Market Technicians Association to aspir-ing Chartered Market Technicians (CMT) exemplifies this tradition.
The shift to an evidence-based objective approach would challengemuch of this material as either meaningless or not sufficiently supportedby statistical evidence. Many of the teachings will go the way of earlyGreek physics and astronomy. Some methods will survive objectificationand statistical testing and will warrant a position in a legitimate body ofTA knowledge.
Lest the reader think my position too harsh, I am not advocating thatthe falsifiability criterion be used to cut off all research in budding TAmethods just as they are being formulated. Many of the brilliant theoriesof science began as half-backed prescientific ideas on the wrong side ofthe falsifiability criterion. These ideas needed time to develop, and oneday some turned into meaningful science. One example in TA is the newfield of socionomics, an outgrowth of Elliott Wave Theory. At the currenttime, I regard this newly developing discipline as prescientific, though itmay have the potential to become a science. According to a conversation Ihad with Professor John Nofsinger, who is working within the field of so-cionomics, at this time the discipline is not yet able to make testable pre-dictions. This will require the quantification of social mood, the keydeterminant of market movement according to socionomics.
Nascent areas of research such as this and others should not be short-circuited simply because they are not at this time able to generate testablepredictions. One day they may be able to do so.
OBJECTIFICATION OF SUBJECTIVE TA: AN EXAMPLE
 
One of the challenging aspects of moving TA to a science will be trans-forming subjective chart patterns into objectively defined testable pat-terns. This section presents an example of how two academictechnicians, Keving Chang and Carol Osler (C&O) objectified the head-and-shoulders pattern).? Not all elements of their pattern are includedhere. Rather, I have included enough of their rules and the problemsthey faced and solved to illustrate the challenges of transforming a sub-jective method into an objective one. For further details please refer totheir original articles.
Descriptions of the head-and-shoulders pattern can be found in manyTA texts® and are typically accompanied by a diagram similar to the onein Figure 3.8. It represents the pattern as a sequence of noise-free priceswings. When the pattern manifests in perfect textbook form, even a be-ginning student of TA can spot it.152 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
The problem occurs when an actual chart pattern departs from thisideal. Even seasoned chartists can debate whether a given pattern quali-fies as a legitimate head and shoulders, an unavoidable consequence ofthe lack of an objective pattern definition. Subjective pattern definitionsgenerally describe how the head-and-shoulders pattern should look, butthey do not provide clear rules for discriminating patterns that do qualifyas head and shoulders from patterns that possess some head-and-shoulders-like features but do not qualify. In other words, the definitions lack clearrules for which patterns to exclude. This problem is conceptualized inFigure 3.6.
Without objective rules for deciding what does and what does notqualify as a legitimate head-and-shoulders pattern it is impossible to eval-uate the pattern’s profitability or predictive power. The solution to theproblem is to define objective rules that discriminate valid head-and-shoulders patterns from those that are not."! This notion is illustrated inFigure 3.7. The challenge of turning a subjective pattern into an objectiveone can be thought of as the problem of defining the pattern as a clearsubset in the super-set of all possible TA price patterns.
C&O defined the head-and-shoulders top pattern as composed of fivepivot or price reversal points that, in turn, define the pattern’s three peaksand two troughs. These pivots are denoted by letters A through E on Fig-ure 3.8. All eight texts consulted by C&O were clear that the head, de-noted by letter C, must be higher than the two surrounding peaks(shoulders) denoted by letters A and E. There has been some debateamong chartists about several auxiliary features including the Adam's ap-ple, the double chin, and the cowlick. However, the TA manuals consultedby C&O were inconsistent on these aspects and they were not included.
 
Set of All Possible Chart Patterns
FIGURE 3.6 Subjective patterns—no definitive exclusion rules.The Scientific Method and Technical Analysis 153
Not H&S
La CeR Mauro Lele)
Double Bottom
Not H&S
 
FIGURE 3.7 Objective patterns—definitive exclusion rules.
One challenge that faces the real-world chartist is the fact that actualprice oscillations do not trace out clearly identifiable peaks and troughs.Rather, peaks and troughs occur at numerous oscillation scales from tinywaves lasting minutes to very large ones lasting years or decades. Thisproperty, called fractal scaling, imposes a burden on the subjective ana-lyst trying to identify a head-and-shoulders pattern. The analyst must visu-ally filter the price behavior to isolate peaks and troughs at one particularscale of interest. This is relatively easy in retrospect, but it is quite difficultas the pattern is actually unfolding in real time.
C&O addressed this problem by using a percentage filter, also knownas an Alexander filter” or a zigzag indicator, which is discussed by Merrill
Price
         
    
          
Left RightShoulder ShoulderA E Neck Line
   
CrossSell Signal
 
BPrior LeftTrough Trough Trough
           
Time
FIGURE 3.8 Head and shoulders.154 METHODOLOGICAL, PSYCHOLOGICAL, PHILOSOPHICAL, STATISTICAL FOUNDATIONS
in Filtered Waves." It is an objective method for identifying peaks andtroughs as prices evolve. Troughs are identified after prices have movedup from a recent price low by an amount greater than a specified thresh-old percentage and peaks are identified after prices have moved downfrom a recent price high by the threshold percentage. The problem is thatthe identification occurs with a time lag, the time it takes for prices tomove the threshold amount. For example, if the threshold is set at 5 per-cent, then a peak is not detected until prices have fallen at least 5 percentfrom the most recent price maximum, and troughs are not detected untilprices have risen at least 5 percent from the recent price minimum. Theminimum required price movement causes a lag between the time thepeak or trough actually occurred and the time at which it is detected bythe zigzag filter.
Next, C&O addressed how to determine the correct threshold per-centage to define the zigzag filter. Different filter thresholds would revealhead-and-shoulders patterns of different size (scale). For example, a 3percent filter might reveal a head-and-shoulders pattern that a 10 percentfilter would completely ignore. This makes it possible for multiple head-and-shoulders patterns of differing scale to exist simultaneously. C&O ad-dressed this problem by subjecting each financial instrument (stock orcurrency) to 10 different zigzag filters employing a range of threshold val-ues. This allowed them to identify head-and-shoulders patterns on a vari-ety of scales.
This raised yet another problem. What should the 10 filter thresholdsbe? Clearly, a set of thresholds that would be good for one instrumentmay not be good for another because they are characterized by differentlevels of volatility. Realizing this, C&O take each instrument’s recentvolatility into account to arrive at the set of 10 filter thresholds used forthat instrument. This insight allowed their head-and-shoulders algorithmto generalize across markets with different volatilities. C&O defined amarket’s volatility, V, as the standard deviation of daily percentage pricechanges over the most recent 100 trading days. The 10 thresholds werear