PeiChann Chang, Professor Information Management Department Yuan Ze University

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Pei-Chann Chang, ProfessorInformation Management
DepartmentYuan Ze University

• Knowledge Discovery in Financial Time Series Data

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Time Series Databases

• A time series is a sequence of real numbers,
  representing the measurements of a real variable
  at equal time intervals
• Stock price movements
• Volume of sales over time
• Daily temperature (Electricity Consumption)
  readings
• Weather data or electrocardiogram (ECG) data
• A time series database is a large collection of
  time series
• all NYSE stocks

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Classical Time Series Analysis

• Identifying Patterns
• Trend analysis
• A companys linear growth in sales over the years
• Seasonality
• Winter sales are approximately twice summer sales
• Forecasting
• What is the expected sales for the next quarter?

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Traffic Speed Time Series

• Non-stationary
• Strong deterministic part
• Weak stochastic part

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Wavelet Transform Denoising (1993,1995)

• Decompose transform the original signal into the
  wavelet domain.
• Threshold suppress small coefficients in the new
  wavelet representation.
• Reconstruct invert back the modified
  representation.

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Multiscale Approximation and Denoising
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• MRA used to obtain the DWT of a discrete signal
  by iteratively applying lowpass and highpass
  filters, and subsequently down sampling them by
  two.
• At each level, this procedure computes

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Figure 1. Computing DWT by MRA
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Wavelet Representations

• Orthogonal representations
• Fast algorithms for decomposition and
  reconstruction
• Restrictions on design of the representation
  functions
• Wavelet representations are not shift invariant

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Time Series Problems (from a databases
perspective)

• The Similarity Problem
• X x1, x2, , xn
• Y y1, y2, , yn
• Define and compute Sim(X, Y)
• E.g. do stocks X and Y have similar movements?

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• Similarity measure should allow for imprecise
  matches
• Similarity algorithm should be very efficient
• It should be possible to use the similarity
  algorithm efficiently in other computations, such
  as
• Indexing
• Subsequence similarity
• clustering
• rule discovery
• etc.

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(b) BLL
(a) MOT
(c) DG
(d) MIR
Figure 1. Instances of Double Bottom pattern.
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Similarity measure

• Given a good data representation, how to choose
  an indexing structure with good performance.
• R-tree, R-tree, R-tree and simple inverted files
  are common choices.

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• Indexing problem
• Find all lakes whose water level fluctuations are
  similar to X
• Subsequence Similarity Problem
• Find out other days in which stock X had similar
  movements as today
• Clustering problem
• Group regions that have similar sales patterns
• Rule Discovery problem
• Find rules such as if stock X goes up and Y
  remains the same, then Z will shortly go down

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Examples

• Find companies with similar stock prices over a
  time interval
• Find products with similar sell cycles
• Cluster users with similar credit card
  utilization
• Cluster products
• Use patterns to classify a given time series
• Find patterns that are frequently repeated
• Find similar subsequences in DNA sequences
• Find scenes in video streams

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Basic approach to the Indexing problem Extract
a few key features for each time series Map
each time sequence X to a point f(X) in the
(relatively low dimensional) feature space,
such that the (dis) similarity between X and Y is
approximately equal to the Euclidean distance
between the two points f(X) and f(Y)
f(X)
X

• Use any well-known spatial access method (SAM)
  for indexing the feature space

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• Scalability an important issue
• If similarity measures, time series models, etc.
  become more sophisticated, then the other
  problems (indexing, clustering, etc.) become
  prohibitive to solve
• Research challenge
• Design solutions that attempt to strike a balance
  between accuracy and efficiency

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Euclidean Similarity Measure

• View each sequence as a point in n-dimensional
  Euclidean space (n length of sequence)
• Define (dis)similarity between sequences X and Y
  as
• Lp (X, Y)

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• Advantages
• Easy to compute
• Allows scalable solutions to the other problems,
  such as
• indexing
• clustering
• etc...

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• Disadvantages
• Does not allow for different baselines
• Stock X fluctuates at 100, stock Y at 30
• Does not allow for different scales
• Stock X fluctuates between 95 and 105, stock Y
  between 20 and 40

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• Normalization of Sequences
• Goldin and Kanellakis, 1995
• Normalize the mean and variance for each sequence
• Let µ(X) and ?(X) be the mean and variance of
  sequence X
• Replace sequence X by sequence X, where
• Xi (Xi - µ (X) )/ ?(X)

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• Similarity definition still too rigid
• Does not allow for noise or short-term
  fluctuations
• Does not allow for phase shifts in time
• Does not allow for acceleration-deceleration
  along the time dimension
• etc .

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Example
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A general similarity framework involving a
transformation rules languageJagadish,
Mendelzon, Milo
Each rule has an associated cost

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Examples of Transformation RulesCollapse
adjacent segments into one segmentnew slope
weighted average of previous slopesnew length
sum of previous lengths
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• Combinations of Moving Averages, Scales, and
  Shifts
• Rafiei and Mendelzon, 1998
• Moving averages are a well-known technique for
  smoothening time sequences
• Example of a 3-day moving average
• xi (xi1 xi xi1)/3

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• Disadvantages of Transformation Rules
• Subsequent computations (such as the indexing
  problem) become more complicated
• Feature extraction becomes difficult, especially
  if the rules to apply become dependent on the
  particular X and Y in question
• Euclidean distances in the feature space may not
  be good approximations of the sequence distances
  in the original space

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Dynamic Time WarpingBerndt, Clifford, 1994

• Extensively used in speech recognition
• Allows acceleration-deceleration of signals along
  the time dimension
• Basic idea
• Consider X x1, x2, , xn , and Y y1, y2, ,
  yn
• We are allowed to extend each sequence by
  repeating elements
• Euclidean distance now calculated between the
  extended sequences X and Y

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Dynamic Time WarpingBerndt, Clifford, 1994
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Restrictions on Warping Paths

• Monotonicity
• Path should not go down or to the left
• Continuity
• No elements may be skipped in a sequence
• Warping Window
• i j lt w
• Others .

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Formulation

• Let D(i, j) refer to the dynamic time warping
  distance between the subsequences
• x1, x2, , xi
• y1, y2, , yj
• D(i, j) xi yj min D(i 1, j),
• D(i 1, j 1), D(i, j 1)

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Solution by Dynamic Programming

• Basic implementation O(n2) where n is the
  length of the sequences
• will have to solve the problem for each (i, j)
  pair
• If warping window is specified, then O(nw)
• Only solve for the (i, j) pairs where i j
  lt w

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Piecewise Linear Representation of Time Series
Time series approximated by K linear segments
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PLR of Financial Time seris
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• Such approximation schemes
• achieve data compression
• allow scaling along the time axis
• How to select K?
• Too small gt many features lost
• Too large gt redundant information retained
• Given K, how to select the best-fitting segments?
• Minimize some error function
• These problems pioneered in Pavlidis Horowitz
  1974, further studied by Keogh, 1997

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Defining Similarity
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Integrating a Wavelet and TSK Fuzzy Rules for
Stock Price Forecasting

• Pei-Chann Chang, Professor
• Information Management Department
• Yuan Ze University

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Outline

• Introduction
• Literature Survey
• Research Approaches
• Simulation Results
• Summary and Future research

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1. Introduction

• Mining stock market tendency is a challenging
  task.
• Many factors influence the performance of a stock
  market including political events, general
  economic conditions, and traders expectations.

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1. Introduction

• Attempts to predict the financial markets,
  ranging from traditional time series approaches
  to artificial intelligence techniques, such as
  fuzzy systems and, artificial neural network
  (ANN) methodologies.

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1. Introduction

• The main drawback with ANNs, and other black-box
  techniques, is the tremendous difficulty in
  interpreting the results
• Do not provide an insight into the nature of the
  interactions between the technical indicators and
  the stock market fluctuations.

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1.Introduction

• New tools and techniques needed in dealing with
  noise, dimensionality, and nonlinearity in stock
  price prediction.
• The proposed framework combines several soft
  computing techniques such as a wavelet transform,
  TSK fuzzy system, data clustering, simulated
  annealing and KNN for Stock forecasting.

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2. Literature Survey

• White 1990 used a feed-forward NN (FFNN) to
  study the IBM daily common stock returns
• Yao and Poh 59 use Technical Indicators (K and
  D) along with price information to predict
  future price values

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2.Literature Survey

• Austin and Looney 8 develop a neural network
  that predicts the proper time to move money into
  and out of the stock market.
• Mingo LÓPEZ et al. 36 use time delay
  connections in enhanced neural networks to
  forecast IBEX-35 (Spanish Stock Index) index
  close prices

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2.Literature Survey

• Nenortaite and Simutis 39 present a trading
  approach based on one-step ahead profit estimates
  created by combining neural networks with
  particle swarm optimization algorithms
• Jaruszewicz and Mandziuk 28 train ANNs using
  both technical analysis variables and intermarket
  data, to predict one day changes in the NIKKEI
  index.

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2.Literature Survey

• The wavelet transform decomposes a process into
  different scales, which makes it useful in
  differentiating seasonalities, revealing
  structural breaks and volatility clusters, and
  identifying local and global dynamic properties
  of a process at these timescales

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2.Literature Survey

• This research, motivated by the effective
  preprocessing capability of wavelets and the
  predictive power of fuzzy rule system, presents a
  hybrid system by integrating the wavelet and a
  TSK fuzzy rule system for stock price prediction.

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3.Methodology

• A time series is a sequence of real numbers,
  representing the measurements of a real variable
  at equal time intervals
• Stock price movements
• Volume of sales over time
• Daily temperature readings
• ECG data
• A time series database is a large collection of
  time series
• all NYSE stocks

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3.Methodology

• The Similarity Problem
• X x1, x2, , xn
• Y y1, y2, , yn
• Define and compute Sim(X, Y)
• E.g. do stocks X and Y have similar movements?

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3.Methodology

• TSK Fuzzy System Based Prediction
• Input Selection Using Stepwise Regression
  Analysis (SRA)
• TSK fuzzy rule systems

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3.Methodology

• Data Preprocessing using Wavelet Theory

Fig1 A Wavelet transform process
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3.Methodology

• Gaussian fuzzy membership functions are adopted

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3.Methodology

• TSK fuzzy rule systems

a set of K IF-THEN rules in the following
form Ri If x1 is Ai1, x2 is Ai2 xn is Ain,
then yi ?i1 ?i1 x1 ?in xn,
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3.Methodology

• Data Clustering
• The K-means clustering algorithm is employed for
  data clustering
• Optimization of the Parameters in Fuzzy Rules
  Using Simulated Annealing

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3.Methodology

• Using K-Nearest-Neighbor as a Sliding Window

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3.Methodology

• Performance Measures
• Mean Absolute Percentage Error (MAPE)

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4.Simulation Results

• The data set applied for test is the TSE index
  and it has been decomposed into two different
  sets the training data, test data.
• The data for TSE index are from July 18, 2003 to
  December 31, 2005, totally 614 records.

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4.Simulation Results

• Before training the TSK fuzzy model, a wavelet
  transformation has been applied to preprocess the
  data. According to the MAPE, a 3-level wavelet
  preprocessing is thus applied.

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4.Simulation Results
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4.Simulation Results

• Six factors selected as the inputs of the TSK
  model to predict the stock price.
• They are six day moving average (MA), six day
  bias (BIAS), six day relative strength index
  (RSI), nine day stochastic line (KD), the moving
  average divergence (MABIAS) and the 13 days
  psychological line (PSY).

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4.Simulation Results

• In the experiment, the stock price data was
  clustered into 2 to 8 clusters. The performance
  (MAPE) of the algorithms with different number of
  clusters is shown in Fig. 6. From the figure, we
  see that the best performance has been achieved
  with 3 clusters

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4.Simulation Results

Fig2 MAPE of the proposed model for different
data clusters.
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4.Simulation Results

• Four different algorithms to be compared with
• the traditional back-propagation neural networks
  (BPN),
• a standard TSK,
• multiple regression model (MRM),
• and a forecasting method by integrating genetic
  algorithm with Wang and Mendals (GAWM)

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4.Simulation Results

Table1. MAPE performance from different methods
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5. Conclusions

• A TSK fuzzy model proposed for stock price
  prediction.
• The data preprocessed using the Haar wavelet.
• Then, SRA technique employed to select the most
  relevant factors for prediction.
• To avoid rule explosion, the k-means clustering
  algorithm employed to group the data into a
  number of clusters and one fuzzy rule is
  generated for each cluster.
• KNN applied for fine-tune the forecasting results.

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5. Future Researches

• A lot of techniques in the Soft Computing or
  Computational Intelligence community on time
  series similarity measures and data forecasting
  problems
• Turning Points prediction instead of stock price
  forecasting
• Simple similarity models that allow efficient
  indexing, and effective retrieving for data
  training.