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Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation Written by Andrew W.Lo, Harry Mamaysky, and Jiang Wang Presented by Xiaodai Guo

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Main Idea of the Paper Combine chart patterns of technical analysis with quantitative trading skills by achieving three sub-goals: I.Smooth the data. II.Define technical patterns mathematically, identify them and use them to do algorithm trading. III.Ways to test the statistical significance of the results (skipped).

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Example: What is a technical pattern: Head and Shoulder Top: a signal for sell

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Part I: Smoothing the data Why smoothing the data? Raw stock price data in reality is very noisy, and to observe the patterns behind the data, we must filter out the noise:

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Part I: Smoothing the data How to smooth the data? A traditional way used by technical analysts to smooth the data: SMA(simple moving average): For any day(Day M): Shortcomings: 1.Every data point is assigned the same weight. 2.At every point of time M, only the information at and before M is used for smoothing.

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Part I: Smoothing the data How to smooth the data? A new way proposed by this paper: A smoothing estimator using Kernel Regression: is a weight which is calculated using the Gaussian kernel.

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Part I: Smoothing the data How to smooth the data? Intuition: For any time point x, its smoothed estimator should be the weighted average of all the time points t in the time window (t ranges 1 to T).

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Part I: Smoothing the data How to smooth the data? (skip) Important formulas: Important concepts: Kernel: a weight function which is constructed from a probability density function. Gaussian Kernel: a weight function which is constructed from the density function of normal distribution.

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Part I: Smoothing the data Example: After smoothing VS before smoothing

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Part I: Smoothing the data Another Example: After smoothing VS before smoothing

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Part II: Identifying patterns A. What is “local extrema” Local maximum(minimum): A day whose stock price is higher(lower) than the stock price of the days before and after it.

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Part II: Identifying patterns B. Define the technical patterns mathematically

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Part II: Identifying patterns B. Define the technical patterns mathematically Head-and-shoulders Reverse head-and-shoulders Broadening tops Broadening bottoms Triangle tops Triangle bottoms Rectangle tops Rectangle bottoms Double tops Double bottoms

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Part II: Identifying patterns C. Test out whether patterns exist in smoothed data How do we look for patterns: For every time window of 38 days, do the smoothing, and then test for patterns using the first 35 days’ smoothed data. Constraint: The last local extrema of the pattern must appear on the 35 th day.

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Part II: Identifying patterns D. Calculate the results How do we trade: According to the author,for every time window of 38 days, if a pattern is observed, we long/short the stock at the closing price of the 38 th day, and close our position at the closing price of the 39 th day. A modification: For every time window of 38 days, if a pattern is observed, we long/short the stock at the closing price of the 39 th day, and close our position at the closing price of the 40 th day.

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Part III: Results A. Calculate the results Implement a back testing using Ford’s daily stock price from 1993/9/24 to 2013/9/24.

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Part III: Results B. The results of back-testing Number of transactions occurred:130 The probability of one transaction to make money:49.2% Mean return of transactions:0.207% Standard deviation of mean return of transactions:0.263% P-value of the mean return under t-test:0.2927

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Part III: Results C. An improved trading strategy An improved trading strategy: After detecting a pattern, instead of holding the stock for one day, we will hold it for five days. The reason for this improvement: Practitioners want to take full advantage of the technical patterns discovered.

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Part III: Results D. Back-testing results of the improved trading strategy Number of transactions occurred:130 The probability of one transaction to make money:53.8% Mean return of transactions:0.816% Standard deviation of mean return of transactions:0.488% P-value of the mean return t-test:0.0986

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Part IV: Pros and cons What we can learn from this paper: How to smooth the data with kernel regression. How to define technical patterns in a numerical way. How to use patterns to trade quantitatively

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Part IV: Pros and cons Criticism: When optimizing the bandwidth h for kernel regression, the author uses the “Cross-Validation” method, which seems to be inappropriate for this problem. Also, the author multiplies this optimized h value by 0.3, which makes this optimization process even less rigorous. Many of the parameters are ad-hoc and come from “empirical experience”, which is not well-explained in this paper. Examples: length of the time window; percentage numbers used in definitions of technical patterns.

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