### Foundations of Technical Analysis: Computational

```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
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
stock price
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).
(x) has a value which is proportional to
2 /2ℎ 2
1
−
−

,
ℎ 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
before smoothing
after smoothing
12
11.5
price
11
10.5
10
9.5
9
0
20
40
60
80
Part I: Smoothing the data
Another Example: After smoothing VS before smoothing
8.8
before smoothing
after smoothing
8.6
8.4
8.2
price
8
7.8
7.6
7.4
7.2
7
6.8
0
10
20
time(day)
30
40
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
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 35th
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 38th day, and close
our position at the closing price of the
39th 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 39th day,
and close our position at the closing price
of the 40th 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.
```