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Can Technical Analysis Be Formalized?

Pring (1980) introduces "technical analysis" and related methods as follows:

The technical approach to investment is essentially a reflection of the idea that the stock market moves in trends which arc determined by changing attitudes of investors to a variety of economic, mone ­tary, political and psychological forces. The art of technical analy ­sis, for it is an art, is to identify changes in such trends at an early stage and to maintain an investment posture until a reversal of that trend is indicated. ... By studying the nature of previous market turning points, it is possible to develop some characteristics which can help identify major market tops and bottoms. Technical analysis is therefore based on the assumption that people will continue to make the same mistakes that they made in the past.'

Clearly, technical analysis covers a broad category of highly subjec ­tive forecasting rules. To simplify the discussion, I first adopt a prelimi ­nary classification. A survey of the literature suggests three major classes to group various forms of technical analysis.

Letting {A',, t = 0, 1, . . .} represent asset prices, the first class of rules issues signals of market turning points using level crossings of the X, process. The level is almost always defined using various local maxima or minima of{X,}. It is the choice of the level that differentiates one rule from another. Figures \u and \b illustrate two examples. The bull (bear) markets are signaled as the Dow-Jones industrials cross trend lines determined by appropriate local maxima (minima). We label this class of rules the trend crossing method.

Figure 2 displays a second major category labeled moving average method. Various moving averages of an observed series are obtained and the intersections of these averages are interpreted as buy and sell signals.

The third group consists of various patterns, whose occurrence is claimed to signal particular types of future behavior by {A",}. Some of these patterns are shown in figure 3. This article argues that, in princi ­ple, all these patterns can be fully characterized using appropriate local minima and maxima. Hence, any pattern can potentially be formalized. However, I show that formal identification of local minima and maxima that can accomplish this is likely to be quite tedious.

Thus, the first step of the analysis is to quantify and formalize, whenever possible, these three categories of technical analysis. I pro ­ceed in two stages. First, I prove that any method that relates to crossings of moving averages constitutes a well-defined prediction methodology. Second, I show that patterns or trend crossings used in obtaining market signals are almost always related to some sequences of local minima and maxima, and, more important, are generally ill defined in their current formulation. I discuss these points using the important notion of Markov times. In fact, one contribution this article makes is to recognize the importance of Markov times as a tool to pick well-defined rules for issuing signals at market turning points.