Title: A Generalized Model for Financial Time Series Representation and Prediction
1A Generalized Model for Financial Time Series
Representation and Prediction
- Author Depei Bao
- Presenter Liao Shu
- Acknowledgement Some figures in this
presentation are obtained from the paper
2Outline of the Presentation
- Introduction
- Critical Point Model (CPM) for Financial Time
Series Representation - Motivation and importance of using critical
points - The generalized CPM to represent financial time
series - Probabilistic model based on CPM for prediction
- Experimental Results
- Conclusion
3Introduction
- Flow Chart of the General Financial Time Series
Prediction Method
Input Data
Feature Extraction
Probabilistic Model
Optimization
Forecast Value
4Introduction
- Main Idea of the Proposed Method Stock movements
are affected by two types of factors - Gradual strength changes between the buying side
and the selling side (Useful Information) - Random factors such as emergent affairs or daily
operation variations (Noise) - Motivation and Goal of the Proposed Method
- Using the original raw price data to do
prediction can be problematic - Remove the noise information and preserve the
useful information to do the prediction
5Critical Point Model (CPM) for Financial Time
Series Representation
- Motivation (Why critical point model?)
- A fluctuant financial time series consists of
a sequence of local maximal/minimal points. Some
of them mirrors the information of trend reversals
6Motivation and Importance of using Critical
Points Pattern Information
- Based on the critical points, the input financial
time series can be represented in a pattern-wised
manner to reflect their trends over different
periods
7CPM Based Representation
- A financial time series is comprised of a
sequence of critical points (local
minimal/maximal) - We only consider the critical points
- Only some of the critical points are preserved
(remove those critical points which are
considered as noise factors)
8Definition of Noise
- Defined based on two measure criterions
- Amount of oscillation between two critical points
- Duration between two critical points
- A small oscillation and a short duration will be
regarded as noise.
9Simple CPM
- Example
-
- Define a minimal time interval T (duration)
and a minimal vibration percentage P
(oscillation). Remove the critical points
(X(i),Y(i)) and (X(i1),Y(i1)) if
10Drawbacks of the Simple CPM
- The Simple CPM is too rough, the critical points
are accessed in a local range (without looking
ahead) - Example of an exception
-
- In this example, it is assume that AB, AD
and BE dont satisfy the removing criteria of the
simple CPM, but BC, CD, DE satisfy
11Drawbacks of the Simple CPM
- Another exception case
- In this example, BC is assumed to be satisfy
the removing criteria of simple CPM
12Drawbacks of the Simple CPM
- Root of the drawback of simple CPM
- Only testing the distance between two successive
critical points to evaluate a vibration - The generalized CPM (GCPM) is proposed in this
paper to overcome these shortcomings
13The Generalized CPM
- The time series is processed sequentially in the
unit of three points (two minimal points and one
maximal point) - Important Reminder in GCPM, the three points in
a unit are not necessary to be successive
critical points
14The Generalized CPM
- Main issues of GCPM
- How to choose the next three-point unit to be
processed - How to choose preserved critical points
15Outline of the GCPM
16Initialization of GCPM
- All the local maximal/minimal points in a raw
time series are extracted to form the initial
critical point series
17Data Representation of GCPM
- After constructing the initial critical point
series C, a critical point selection criteria is
applied to filter out the critical points
corresponding to noise. Then the original time
series is approximated by linear interpolating
points between a maximal point and a minimal point
18The Critical Point Selection Criteria of GCPM
- The first and the last data point in the original
time series are preserved as the first and last
point in C - Local maximal and local minimal points in the
approximated series must appear alternately
19The Critical Point Selection Criteria of GCPM
- Selection is also based on the oscillation
threshold P and the duration threshold T - Consider P first, there are four cases
- Both the rise and the decline oscillations exceed
P - The rise over P, but the decline below P
- The decline over P, but the rise below P
- Neither the rise nor the decline over P.
20Four Cases Regard to Oscillation
21Second Layer Checking with Duration T
- For the oscillation below P but the duration
above T, it still holds valuable trend
information - Case 2 and Case 3 pass the duration T checking
will be considered as Case 1 - For Case 4, if any side pass the duration T
checking, the midpoint will be removed and choose
the next test unit beginning with the current
third point
22Process for Case 1
- The first two points, i, i1 will be preserved,
and then the next unit will be i2,i3,i4
23Process for Case 2
- Two sub-cases
- If Y(i3) gt Y(i1), the next unit will be i,
i3, i4 - Otherwise, the next unit will be i, i1, i4
24Process for Case 3
- Two sub-cases
- Y(i3)gtY(i1)
- Y(i3)ltY(i1)
- The next unit will always be i2,i3,i4 because
Y(i2)ltY(i)
25Process for Case 4
- Two sub-cases
- Y(i)ltY(i2) next unit will be i, i3, i4
- Y(i)gtY(i2) next unit will be i2, i3, i4
26Price Pattern Matching in GCPM
- Two types of patterns
- The point-wise patterns
- The trend pattern
27Price Pattern Matching in GCPM
- An example of finding a constraint H S pattern
28Price Pattern Matching in GCPM
- Numerical formulation of the constraint H S
pattern
29Probabilistic model based on GCPM for prediction
- After the data smoothing and GCPM process, five
common technical analysis systems including 30
technical indicators are used to represent the
each turning point. - Price pattern system
- Trendline system
- Moving average system
- RSI oscillator system
- Stochastic SlowK-SlowD oscillator system
- The turning points and their technical indicators
are used as training examples to learn the
parameters of a probabilistic model based on the
Markov Network
30Probabilistic model based on GCPM for prediction
- The Markov Network
- Y true,false represent whether a critical
point is the real turning point - X X1,X2,,Xn, Xi true,false is a vector
with Xi represents the i-th technical indicator
and TRUE for the occurrence of the signal for the
current critical point
31Probabilistic model based on GCPM for prediction
- The Markov Network Can be Converted to
- For each indicator, if the corresponding rule Xi
-gt Y (Xi V Y) is true, then fi(xi,y) 1,
otherwise fi(xi,y) 0. The to-be-estimated
parameter wi corresponds to each rule.
32Optimization of Parameters
- The parameter wi of the probabilistic model is
learned by optimizing the conditional
log-likelihood (CLL) - n is the number of training samples.
- After obtaining the optimal parameters, the
inference step is calculated by using the Gibbs
sampling method (a special Markov Chain Monte
Carlo algorithm)
33Experimental Results
- The approximation accuracy of GCPM, the
normalized error (NE) is adopted as the metric - NE for approximating the prices of IBM
34Experimental Results
- Graphical comparison between the simple CPM and
the proposed GCPM to model the IBM price series
35Experimental Results
- Test on Stock Trading
- A simple trading rule if the current reversal is
from an uptrend to a downtrend over a certain
probability estimated by the proposed model, then
sell, and vice versa. With initial fund 1000 - Trading log of ALCOA INC for 4 years
36Experimental Results
- Test the system on the CBOT Soybeans future
prices from 1/5/1970 to 12/21/2006
37Experimental Results
- The system is also evaluated for the simulated
trades on 454 stocks of the SP 500c. Then stocks
are randomly picked and examine their profits on
three periods
38Conclusion
- This paper proposed a new financial time series
representation method for prediction based on the
generalized critical point model (GCPM) - The GCPM based representation is general and
robust - Experimental results demonstrated that even in a
period where a stock has a significant downtrend,
the proposed method can still make profits.
39End of My Presentation