Presented by
Xiaodai Guo

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).

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

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:
12.5
12
11.5
11
10.5
10
9.5
9
0 10 20 30 40 time(day)
50 60 70 80

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.

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.

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).
𝜔 𝑡
(x) has a value which is proportional to
1 ℎ 2𝜋 𝑒 − 𝑥−𝑡
2
/2ℎ
2
, so the farther t is from x, the less weight point t will have when used for estimating x.

Part I: Smoothing the data
How to smooth the data? (skip)
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.
Important formulas:

Part I: Smoothing the data
Example: After smoothing VS before smoothing
12.5
12
11.5
11
10.5
10
9.5
9
0 20 40 time(day)
60 80 before smoothing after smoothing

Part I: Smoothing the data
Another Example: After smoothing VS before smoothing
7.8
7.6
7.4
7.2
7
8.8
8.6
8.4
8.2
8
6.8
0 10 20 time(day)
30 40 before smoothing after smoothing

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.

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

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

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.

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.

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.

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

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.

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

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

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.