Market timing: a test of a charting heuristic – Technical Analysis
In addition to the use of metric-based trading rules, technical analysis …
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Economics Letters 77 (2002) 55-63
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Market timing: a test of a charting heuristic
William Leigh a , *, Noemi Paz a , Russell Purvis b
Department of Management Information Systems, College of Business, University of Central Florida, Box 161400, Orlando, FL 32816 -1400, USA b Clemson University, Clemson, SC, USA Received 16 August 2001; received in revised form 4 March 2002; accepted 12 March 2002
Abstract We implement a graphical (or `charting\’) heuristic, the `bull flag\’, which accepts a particular pattern of historical prices as a signal for a future market price increase, test it with several years of New York Stock Exchange Composite Index history, and find positive results. The results support the validity of technical analysis for stock market price prediction and fail to confirm the efficient markets hypothesis. 2002 Elsevier Science B.V. All rights reserved.
Keywords: Technical trading; Security markets JEL classification: G14
1. Introduction One interpretation of the efficient markets hypothesis is that market prices follow a random walk and cannot be predicted based on their past behavior. Discoveries of `anomalies\’, relationships that can be used to earn abnormal returns and appear to violate the efficient markets hypothesis, are numerous in the finance literature. Well-known anomalies involve: unexpected earnings announcements, firm size, month of January, day of the week, analysts\’ recommendations, impact of the federal budget deficit announcement, and others. Frankfurter and McGoun (2001) survey the anomalies literature and discuss the paradigmatic crisis in academic finance which they represent. Stock market forecasters who practice technical analysis concern themselves with the dynamics of the market price and volume behavior itself, rather than with the fundamental economic nature of specific securities that are traded. Charles Dow published the original Dow Theory for technical analysis in 1884, and a modern explication is found in Edwards and Magee (1997). The efficient
* Corresponding author. Tel.: 1 1-407-823-3173; fax: 1 1-407-823-2389. E-mail address: firstname.lastname@example.org (W. Leigh). 0165-1765 / 02 / $ – see front matter PII: S0165-1765( 02 )00110-6 2002 Elsevier Science B.V. All rights reserved.
W. Leigh et al. / Economics Letters 77 (2002) 55 – 63
markets hypothesis implies that the technical approach to market price prediction is invalid. However, positive reports as to the effectiveness of metric-based trading rules, such as momentum measures and moving averages, which use only historical price and volume information and are considered by many to be `technical\’ rules, have appeared more than once and recently in the most respected finance journals. Hong et al. (2000) and Hong and Stein (1999) examine trading rules that use measures of momentum. Gencay (1998) reports positive results with metric-based technical trading rules implemented with nonparametric models. Neftci (1991), Brock et al. (1992), and an increasing number of others, look at technical trading rules and report positive results. In addition to the use of metric-based trading rules, technical analysis includes charting heuristics. Charting heuristics are used to identify certain graphical patterns in historical price and volume time series data that are considered to be signals to buy (or sell). Lo et al. (2000) test charting heuristics using kernel regression for pattern identification and find marginally positive results. Neftci (1991) discusses the difficulties that the conventional methods of finance, based on linear models, have in describing typical stock market activity of interest to stock traders: the recognition of sporadic buy and sell signals, and the recognition of patterns in time series. In this paper we illustrate the use of template matching, a basic technique from pattern recognition, to implement a charting trading heuristic from technical analysis. This approach may provide the nonlinear and rule-based method that Neftci (1991) is seeking. We present results from testing one variation of one technical analysis pattern, the `bull flag.\’ The definition of `flag\’ from Downes and Goodman (1998): `FLAG–technical chart pattern resembling a flag shaped like a parallelogram with masts on either side, showing a consolidation within a trend. It results from price fluctuations within a narrow range, both preceded and followed by sharp rises or declines.\’ A bull flag pattern is then a horizontal or downward sloping flag of `consolidation\’ followed by a sharp rise in the positive direction, the `breakout.\’ In this paper we concentrate on this particular pattern, the bull flag, because the results are crisp and persuasive. (In addition to the particular variation of the bull flag pattern presented in this paper, we looked at other patterns applied to both price and volume and achieved mixed results.) We have found no rigorous testing of this particular charting pattern anywhere in the academic literature. We implement the bull flag charting heuristic through use of a template matching technique from pattern recognition and test the resulting market price forecasts against the overall average price increase experienced in the period we are using for several prediction horizons (10, 20, 40, and 80 trading days). We work with the New York Stock Exchange Composite Index, and for this work with a broad-based composite index, the overall average price (index value) increase / decrease in the period is equivalent to the return from a buy-and-hold or random-selection trading strategy, which are implied as optimal by the random walk model of the efficient markets hypothesis. We use the values of the New York Stock Exchange Composite Index for the period from 8 / 6 / 80 to 9 / 15 / 99 for testing and compute a value for how well a template representation of the bull flag pattern fits or matches the 40 trading day window ending with each of the 4817 trading days in the test period. The computed fit values are used in trading rules of the sort: `If the fit value for a trading day exceeds a set value then buy on that trading day and hold for some number of days.\’ If the average of the returns in a test period from simulated trades using this rule exceeds the average of returns which would have accrued to buying on every day in the period of comparison by a statistically significant amount, then we have found a successful forecasting method based only on price history; this finding fails to confirm the efficient markets hypothesis (specifically, the weak form) and contributes in an important way to the growing `anomalies\’ literature.
W. Leigh et al. / Economics Letters 77 (2002) 55 – 63
Fig. 1. 10 3 10 grid of weights used in this study to represent the bull flag charting pattern. This template is fitted or matched to 4817 40 trading day wide windows, each fitting window ending on one of the 4817 trading days in the period of the study. The hypothesis is that good fits are indications of buying opportunities.
2. Method Fig. 1 shows the template, T, that we use for the bull flag charting pattern. This is a 10 3 10 grid with weights, w ij , ranging from 2 2 to 1 4 in the cells. The weighting values define areas in the template for the horizontal consolidation (first seven columns) and for the upward-tilting breakout (last three columns) portions of this bull flag pattern, which are also indicated by the graying in the figure. The bull flag pattern template, T, is fitted / matched to the NYSE Composite Index\’s time series closing price data 4817 times by fitting a window of 40 price values to the template starting with the oldest price and moving the window up one trading day for each of the next 4816 fittings. The procedure used to accomplish the fitting is template matching (Duda and Hart, 1973), a pattern recognition technique used to match a template to a pictographic image to identify objects. We let pt be the composite\’s price value on trading day t for the fitting window ending on trading day k, where t 5 2 39, . . . , 0, k 5 1, . . . , 4817, and k 5 1 is the oldest price. For each trading day k we synthesize a 10 3 10 image grid, Ik , from each set of 40 closing price values. Next, we compute a crosscorrelation of the bull flag template T with the image grid Ik and calculate two output values for each fitting: FIT k and HEIGHT k . The following is a specification for the template matching process for a single 40 trading day window. Within each 40-day window of data, we `Winsorize variances\’ (Roberts, 1995, p. 150) to remove the worst noise by replacing every observation which is beyond two standard deviations from the mean of the price values in the window with the respective two standard deviation boundary value. The next step is to take the 40 days of closing prices and map the information into a 10 3 10 image grid for the fitting window ending with trading day k. Let the image grid\’s gray scale values, gij , be the individual values computed into each cell of the 10 3 10 image grid, Ik . First we define how the price values will relate to the rows in the grid by calculating the range of the 40 prices and dividing the range by 10 to arrive at an increment value: inc 5 ( pmax 2 pmin ) / 10 pmax and pmin are the maximum and minimum price values found within the 40 values in each window. Using this increment, we associate a row i with an interval:
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