Foundations of Technical Analysis

Computational Algorithms, Statistical Inference, and

Empirical Implementation

Author(s): Andrew W. Lo, Harry Mamaysky and Jiang WangSource: 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 volumee.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).

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

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- FrequencyNYSE/AMEX

Nasdaq

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

Empirical Result- Descriptive Summary NYSE/AMEX

Nasdaq

Different conditional mean, standard deviation, skewness and kurtosis

Not all consistent between NYSE/AMEX and 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

of the conditional returns

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.

Thanks!