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A Generalized Model for Financial Time Series Representation and Prediction

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Title: A Generalized Model for Financial Time Series Representation and Prediction


1
A 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

2
Outline 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

3
Introduction
  • Flow Chart of the General Financial Time Series
    Prediction Method

Input Data
Feature Extraction
Probabilistic Model
Optimization
Forecast Value
4
Introduction
  • 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

5
Critical 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

6
Motivation 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

7
CPM 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)

8
Definition 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.

9
Simple 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

10
Drawbacks 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

11
Drawbacks of the Simple CPM
  • Another exception case
  • In this example, BC is assumed to be satisfy
    the removing criteria of simple CPM

12
Drawbacks 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

13
The 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

14
The Generalized CPM
  • Main issues of GCPM
  • How to choose the next three-point unit to be
    processed
  • How to choose preserved critical points

15
Outline of the GCPM
16
Initialization of GCPM
  • All the local maximal/minimal points in a raw
    time series are extracted to form the initial
    critical point series

17
Data 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

18
The 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

19
The 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.

20
Four Cases Regard to Oscillation
21
Second 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

22
Process for Case 1
  • The first two points, i, i1 will be preserved,
    and then the next unit will be i2,i3,i4

23
Process 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

24
Process 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)

25
Process 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

26
Price Pattern Matching in GCPM
  • Two types of patterns
  • The point-wise patterns
  • The trend pattern

27
Price Pattern Matching in GCPM
  • An example of finding a constraint H S pattern

28
Price Pattern Matching in GCPM
  • Numerical formulation of the constraint H S
    pattern

29
Probabilistic 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

30
Probabilistic 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

31
Probabilistic 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.

32
Optimization 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)

33
Experimental Results
  • The approximation accuracy of GCPM, the
    normalized error (NE) is adopted as the metric
  • NE for approximating the prices of IBM

34
Experimental Results
  • Graphical comparison between the simple CPM and
    the proposed GCPM to model the IBM price series

35
Experimental 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

36
Experimental Results
  • Test the system on the CBOT Soybeans future
    prices from 1/5/1970 to 12/21/2006

37
Experimental 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

38
Conclusion
  • 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.

39
End of My Presentation
  • Thank you!
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