1. 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

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

3. 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

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

5. 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)

6. 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).

7. 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

8. 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

9. 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

10. 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).

11. 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:

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

13. 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).

14. Examples of Kernel Regression

15. 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)

16. Patterns Recognition-HS

17. Patterns Recognition-BTOP

18. 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

19. 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

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

21. 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

22. 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

23. 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

24. 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

25. 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.

26. Thanks!