Foundations of Technical Analysis Computational Algorithms, Statistical Inference, and Empirical Implementation Author(s): Andrew W. Lo, Harry Mamaysky and Jiang Wang Source: The Journal of Finance, Vol. 55, No. 4 (Aug., 2000) Presenter: Rey Zong Lei

Outline Background Objectives Literature Review Data Data source, resampling and smoothing Automatic Technical Pattern Recognition Empirical Result and Conclusion Comment and Critique

Objectives Propose an automatic approach to recognize technical patterns Apply method to US stock data to check effectiveness of traditional technical indicators Key words: Smooth estimator- Kernel regression Technical indicators- head-and-shoulders, double-bottoms

Examples of Technical Charts e.g.2 Price and volume e.g.1 Head-and-Shoulders

Literature review Academic unacceptance and professional availability "voodoo finance“ “Under scientific scrutiny, chart-reading must share a pedestal with alchemy.” - A Random Walk down Wall Street, Burton Malkiel (1996)

Literature review -continued Lo and MacKinlay (1988, 1999): It rejected the Random Walk Hypothesis for weekly U.S. stock indexes, and past prices may be used to forecast future returns to some degree. Indirect supportive studies: Treynor and Ferguson (1985); Brown and Jennings (1989); Jegadeesh and Titman (1993); Blume, Easley, and O'Hara (1994); Chan, Jegadeesh, and Lakonishok (1996); Lo and MacKinlay (1997); Grundy and Martin (1998) and Rouwenhorst (1998). Direct supportive studies Pruitt and White (1988); Neftci (1991); Brock, Lakonishok, and LeBaron (1992); Neely, Weller, and Dittmar (1997); Neely and Weller (1998); Chang and Osler (1994); Osler and Chang (1995) and Allen and Karjalainen (1999).

Structure Data Preparation - Resampling, Smoothing and Kernel Regression Automatic Technical Patterns Recognition - Head-and-shoulders, broadening tops, triangle, etc Probability Distribution Comparison - Conditional, unconditional returns and Monte Carlo Simulation - Goodness-of-Fit Tests, Kolmogorov-Smirnov test

Data Specification Data : daily returns of individual NYSE/AMEX and Nasdaq stocks Time Period: From 1962 to 1996 Source: Center for Research in Securities Prices (CRSP). Annotation: Split into NYSE/AMEX and Nasdaq Split into seven five-year periods: 1962 to 1966, 1967 to 1971… Split into five market capitalization quantiles

Data Preparation- Resampling Randomly selected 10 stocks from each of five market capitalization quantiles Restriction that at least 75 percent of the price observations must existed Observed the sample of 50 across seven time sub-periods Repeated the process again for robustness

Data Preparation- Smoothing Smoothing Estimators Non-linear relations: Natural estimator of the function m (-) at the point xo Assumed that the function m (-) is sufficiently smooth, then for time-series observations Xt near the value xo, the corresponding values of Pt should be close to m(xo).

Data Preparation- Smoothing Kernel Regression Weight function wt (x) is constructed from a probability density function K(x), also called a kernel: Or So the weights are:

Data Preparation- Smoothing Kernel Regression Apply Kernel Regression to our estimation of the non-linear function, Where the authors adopted the Gaussian kernel:

Data Preparation- Smoothing Calibration for Kernel Regression We need to decide the optimal parameter h, also called bindwidth Method: minimize the cross-validation function: Result: “Bandwidths too large”, “Fitted values are too smooth” Used a bandwidth of 0.3 x h*, where h* minimizes CV(h).

Examples of Kernel Regression

Patterns Recognition Five Pairs of most popular technical patterns Head-and-shoulders (HS) and inverse head-and-shoulders (IHS) Broadening tops (BTOP) and bottoms (BBOT) Triangle tops (TTOP) and bottoms (TBOT) Rectangle tops (RTOP) and bottoms (RBOT) Double tops (DTOP) and bottoms (DBOT)

Patterns Recognition-HS

Patterns Recognition-BTOP

Probability Distribution Comparison Compare standardized unconditional and conditional returns Rolling window of 35 days to detect technical patterns Conditional returns: the returns in 3 days after the completion of the technical patterns Goodness-of-Fit Tests Kolmogorov-Smirnov test

Empirical Result- Frequency NYSE/AMEX The most common is double tops and bottoms, and the second most common are head-and-shoulders and inverted head-and-shoulders Difference between NYSE/AMEX and Nasdaq Frequency is not evenly distributed between increasing and decreasing volume-trend cases. More patterns than the sample of simulated geometric Brownian motion Nasdaq

Empirical Result- Descriptive Summary NYSE/AMEX Different conditional mean, standard deviation, skewness and kurtosis Not all consistent between NYSE/AMEX and Nasdaq Nasdaq

Empirical Result- Goodness-of-Fit Tests NYSE/AMEX Nasdaq NYSE/AMEX 7 patterns had significantly different relative frequencies of the conditional returns HS, IHS, BTOP, TBOT, RTOP, RBOT, DTOP Nasdaq All patterns had significantly different relative frequencies Technical Patterns better apply to the Nasdaq stocks

Empirical Result- Kolmogorov-Smirnov test NYSE/AMEX Five patterns were significant HS, BBOT, RTOP, RBOT and DTOP Condition on declining volume trend, the statistical significance declines for most patterns The difference between the increasing and decreasing volume-trend conditional distributions is statistically insignificant Explanation: The relatively small sample sizes lead to the lack of power of the Kolmogorov-Smirnov test

Conclusions It is possible to automatically identify regularities by extracting nonlinear patterns from noisy data Certain technical patterns do provide incremental information, especially for Nasdaq stocks, although this does not necessarily imply that technical analysis can be used to generate "excess" trading profits

Comment Successful application of automatic technical patterns recognition Robustness with in-the-sample and out-of-sample validation Detailed comparison between sub-datasets across time periods, company market capitalization, volume trend cases, NYSE/AMEX and Nasdaq markets

Critique Human model manipulation Arbitrarily decided using 0.3 h* for Kernel Regression Severe sample selection bias: 50 random companies- industries? Business cycles? Performance? 7 time periods – market structure unchanged? 35 trading days – shorter term or longer terms? 1 day return after 3 lag days – why not using the average return? No strong implications: Whether each technical pattern is associated with a significant positive abnormal return or a negative one? Pure explanatory model with no predictive effect, or any guidance for business implementation. No explanation why technical analysis worked.

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