vii
TABLE OF CONTENTS
CHAPTER
1 1
2
DECLARATION
DEDICATION
ACKNOWLEDGEMENT
ABSTRACT
ABSTRAK
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
TITLE
LIST OF ABBREVIATIONS
INTRODUCTION
1.1
The Background of Study
1.2
Problem Statement
1.3
The Significance of the Research
1.4
1.5
1.6
Research question
Objective of study
Scope of study
LITERATURE REVIEW
2.1
Fuzzy time series survey
2.1.1
Statistics about FTS
2.1.1.1
Results and discussions of FTS survey
2.2
Highlighted Studies of FTS
2.3
Some gaps in FTS
12
13
14
7
7
12
5
6
6
3
5
1
1 vi vii x xiv xv ii iii iv v
3 3 METHODOLOGY
3.1
Introduction
3.2
Fuzzy Logic, Fuzzy Set and Fuzzy relationship
23
23
23

viii
3.3
Fuzzy membership function
3.4
Membership Value Assignments
3.5
Intuition
3.6
Fuzzy Time Series
3.6.1
Fuzzy time series definitions
3.6.1.1
The algorithm of Chen’s first-order model
3.6.1.2
The algorithm of Yu’s model
3.6.1.3
Exponentially weighted algorithm
(Lee’s model)
3.7
Proposed algorithms and methods
3.7.1
Polynomial Fuzzy Time Series
3.7.1.1
TAIEX forecasting
3.7.2
Definitions and algorithm for differential fuzzy time series model
3.7.3
3.7.4
3.7.5
28
29
36
3.7.2.1
Algorithm of deferential fuzzy time series model
3.7.2.2
Enrollment Forecasting
3.7.2.3
TAIEX Forecasting using differential fuzzy time series
Data preprocessing in fuzzy time series
3.7.3.1
Effective length of interval for the
38
39
41
43 proposed model
3.7.3.2
Empirical works
44
45
Multi-layer stock forecasting fuzzy time series 48
3.7.4.1
The framework of the proposed
Multi-layer stock forecasting model 50
3.7.4.2
Data 52
3.7.4.3
Empirical works
K-step-ahead forecaster fuzzy time series
3.7.5.1
Proposed revised algorithm based on Yu’s and Lee’s models for k-step-
52
56 ahead STLF using original load data 57
3.7.5.2
Proposed revised algorithm of Yu’s and Lee’s models for k-step-ahead
STLF when using processed load data
3.7.5.3
Illustrative Example
58
61
30
31
31
34
24
25
25
26
26

4 4 ix
DISCUSSION AND RESULTS
4.1
Polynomial fuzzy time series
4.1.1
4.1.2
Empirical analyses
Certain discussions of polynomial FTS
4.1.2.1
Preference of polynomial fuzzy time series over fuzzy time series
4.1.2.2
Resolving over-fitting in proposed models
4.1.2.3
Optimization costs
4.2
Differential fuzzy time series
4.2.1
4.2.2
Empirical analyses
The differential FTS model explanation and remarks
4.3
Data pre-processing in FTS
4.3.1
Comparison of results
4.4
Multi-layer stock market fuzzy time series model
4.4.1
Illustrative experiments
4.4.2
Remarks, findings and discussions of the
Multi-layer stock market fuzzy time series model
4.5
K-step-ahead forecaster fuzzy time series
4.5.1
Model selection
4.5.2
Model verification and discussion
64
64
64
66
66
78
86
86
87
67
68
70
71
71
75
75
77
77
5 5 5 CONCLUSIONS
5.1
Polynomial FTS
5.2
Differential FTS
5.3
Conclusion and future work of data pre-proccessing
FTS model
5.4
Multi-layer FTS model
5.5
K-step-ahead forecaster FTS model
5.6
Highlights of the Study
95
95
96
96
96
97
98
REFERENCES
REFERENCES
REFERENCES
99

x
LIST OF TABLES
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
4.1
4.2
4.3
4.4
4.5
4.6
TABLE NO.
2.1
2.2
4.7
4.8
4.9
4.10
TITLE PAGE
Certain statistics about important FTS studies
Comparison of method with a same length of intervals but different starting points from 1990 to 1999
Fuzzy sets and fuzzy relationship for TAIEX
Differential fuzzy set and establishing DFLRs of enrolment
Differential fuzzy logic relationship group of enrollment
Fuzzy sets and differential fuzzy set of TAIEX for 1997
FLR and DFLR of TAIEX for 1997
DFLRG of TAIEX for 1997
Fuzzified transformed time series for 1998
First order fuzzy logical relationships for training dataset for
1998
Fuzzy Logical Relationship Groups for 1998
Fuzzified transformed time series for 1998
Different length of intervals for TAIEX
Different length of intervals for NASDAQ
Different length of intervals for DJI
Different length of intervals for S&P 500
OL s, T RP s, T RP F s, and FLRs for Group I
Comparison of RMSEs between different methods
MAPEs of STLF forecasting
Evaluation of RMSEs of TAIEX from 1990 to 1995
Evaluation of RMSEs of TAIEX from 1996 to 1999
Average of RMSEs from 1991 to 1999
Comparison of forecasting accuracy (MSEs) of proposed method for enrollment
Forecasting RMSEs from 1990 to 1994
Forecasting RMSEs from 1995 to 1999
Average of RMSEs from 1990 to 1999
Forecasting MAPEs
21
73
76
76
76
76
42
43
43
47
22
35
40
41
55
55
55
62
68
47
48
49
54
69
72
72
73

4.21
4.22
4.23
4.24
4.25
4.17
4.18
4.19
4.20
4.26
4.27
4.28
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
xi
Forecasting RMSEs from 1995 to 1999
Average of RMSEs from 1990 to 1999
Forecasting MAPEs
Yu’s method ( 2005 ) different RMSEs on TAIEX from 1990-
1995 for original data
Yu’s method ( 2005 ) different RMSEs on TAIEX from 1995-
1999 for original data
Average of Yu’s method ( 2005 ) different RMSEs on TAIEX from 1990-1999 for original data
Yu’s method ( 2005 ) different RMSEs on NASDAQ from 1990-
1995 for original data
Yu’s method ( 2005 ) different RMSEs on NASDAQ from 1995-
1999 for original data
Average of Yu’s method ( 2005 ) different RMSEs on NASDAQ from 1990-1999 for original data
Yu’s method ( 2005 ) different RMSEs on DJI from 2000-2004 for original data
Yu’s method ( 2005 ) different RMSEs on DJI from 2005-2009 for original data
Average of Yu’s method ( 2005 ) different RMSEs on DJI from
2000-2009 for original data
Yu’s method ( 2005 ) different RMSEs on S&P500 from 2000-
2004 for original data
Yu’s method ( 2005 ) different RMSEs on S&P500 from 2005-
2009 for original data
Average of Yu’s method ( 2005 ) different RMSEs on S&P500 from 2000-2009 for original data
Yu’s method ( 2005 ) different RMSEs on TAIEX from 1990-
1995 for pre-processed data
Yu’s method ( 2005 ) different RMSEs on TAIEX from 1995-
1999 for pre-processed data
Average of Yu’s method ( 2005 ) different RMSEs on TAIEX from 1990-1999 for pre-processed data
Yu’s method ( 2005 ) different RMSEs on NASDAQ from 1990-
1995 for pre-processed data
Yu’s method ( 2005 ) different RMSEs on NASDAQ from 1995-
1999 for pre-processed data
Average of Yu’s method ( 2005 ) different RMSEs on NASDAQ from 1990-1999 for pre-processed data
76
76
76
79
79
79
80
80
80
80
81
81
81
81
82
83
83
83
83
84
84

4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.50
4.29
4.30
4.31
4.32
4.33
xii
Yu’s method ( 2005 ) different RMSEs on DJI from 2000-2004 for pre-processed data
Yu’s method ( 2005 ) different RMSEs on DJI from 2005-2009 for pre-processed data
Average of Yu’s method ( 2005 ) different RMSEs on DJI from
2000-2009 for pre-processed data
Yu’s method ( 2005 ) different RMSEs on S&P500 from 2000-
2004 for pre-processed data
Yu’s method ( 2005 ) different RMSEs on S&P500 from 2005-
2009 for pre-processed data
84
84
85
85
85
Average of Yu’s method ( 2005 ) different RMSEs on S&P500 from 2000-2009 for pre-processed data
MAPE2s for 2-step-ahead (one-hour) forecasting Group I-II
85
88
MAPE2s for 2-step-ahead (one-hour) forecasting Group III-IV 88
Average of MAPE2s for 2-step-ahead (one-hour) Group I-IV 88
MAPE12s for 12-step-ahead (six-hour) forecasting Group I-II 89
MAPE12s for 12-step-ahead (six-hour) forecasting Group III-IV 89
Average of MAPE12s for 12-step-ahead (six-hour) forecasting
Group I-IV 89
MAPE24s for 24-step-ahead (twelve-hour) forecasting of
Group I-II
MAPE24s for 24-step-ahead (twelve-hour) forecasting of
89
Group III-IV
Average of MAPE24s for 24-step-ahead (twelve-hour)
89 forecasting Group I-IV 89
MAPE48s for 48-step-ahead (one-day) forecasting of Group I-II 90
MAPE48s for 48-step-ahead (one-day) forecasting of Group
III-IV
Average of MAPE48s for 48-step-ahead (one-day) forecasting of Group I-IV
Evaluation of the results of algorithm 4.2 for 5 successive days for group III
90
90
91
Evaluation of the results of algorithm 4.2 for 5 successive days for group I
Evaluation of the results of algorithm 4.2 for 5 successive days for group I
Evaluation of the results of algorithm 4.2 for 5 successive days for group II
91
91
92

4.51
4.52
4.53
4.54
4.55
xiii
Evaluation of the results of algorithm 2 for 5 successive days for group III
Evaluation of the results of algorithm 2 for 5 successive days for group III
Evaluation of the results of algorithm 2 for 5 successive days for group IV
Evaluation of the results of algorithm 2 for 5 successive days for group IV
Evaluation of the results of algorithm 2 for 5 successive days for group III
92
92
92
92
93

xiv
LIST OF FIGURES
4.7
4.8
4.9
4.10
4.11
FIGURE NO.
3.5
3.6
3.7
4.1
4.2
4.3
3.1
3.2
3.3
3.4
4.4
4.5
4.6
TITLE PAGE
Sample of fuzzy membership function
Proposed multi-layer model
Unprocessed data for year 2002 of DJI
Processed data for year 2002 of DJI
Original load data from group I
Processed load data from group I
Comparison using Lee’s method from group I
Comparison of RMSEs by the average-based
Comparison of RMSEs by the distribution-based
Comparison between actual and forecasts of normal day
(group 1)
Comparison between actual and forecasts of special day
(group 4)
Detecting trends approach, between normal FLRGs for
70
70 enrollment
Detecting trends approach, between differential FLRGs for
74 enrollment 74
MAPEs obtained by applying deterrent methods for group I 93
MAPEs obtained by applying deterrent methods for group II 93
MAPEs obtained by applying deterrent methods for group III 93
MAPEs obtained by applying deterrent methods for group IV 94
Comparison of electricity usage between 12/25/06 and 12/18/06 94
59
59
63
69
69
26
51
53
53

xv
LIST OF ABBREVIATIONS
FLR
FLRG
FOREX
FSFTS
FTS
HHLD
ICT
ANN
CPDA
DBFTS
DJI
DSL
DVL
FL
KOSPI
MAPE
MSE
MaxAPE24 -
-
-
-
MinAPE48 -
MLR -
NASDAQ -
-
-
-
-
-
-
-
-
-
-
-
-
-
-
NN
LHS -
-
Artificial Neural Network
Cumulative Probability Distribution Approach
Distance Based Fuzzy Time Series
Dow Jones Industrial average
Digital Subscriber Line
Deterministic Vector Long-Term forecasting
Fuzzy Logic
Fuzzy Logical Relationship
Fuzzy Logical Relationship Group
FOReign EXchange market
Fuzzy Stochastic Fuzzy Time Series
Fuzzy Time Series
Half Hourly Load Data
Information Communications Technology
Korea Composite Stock Price Index
Mean Absolute Percentage Error
Mean Square Error
Maximum of Absolute Percentage Error for 24 steps ahead
Minimum of Absolute Percentage Error for 48 steps ahead
Multiple Regression Model
National Association of Securities Dealers Automated
Quotations
Nural Network
Left Hand Side

LHS
OL
PL
RHS
RMSE
S and P500 -
SBI -
STLF
TAIFEX
TAIEX -
-
-
-
-
-
-
-
UDM
WCDT -
-
Left Hand Side
Original Load data
Processed Load data
Right Hand Side
Root of Mean Square Error
Standard and Poor’s 500
State Bank of India
Short Term Load Forecasting
Taiwan Futures Exchange
Taiwan Stock Exchange Capitalization Weighted Stock
Index
Uniform Discretion Method
Weighted C-fuzzy Decision Tree xvi