Advances in Time Series Forecasting

196 Pages·2017·8.55 MB·English

by  Cagdas Hakan Aladag

Advances in Time Series
Forecasting
(Volume 2)
Edited by
Cagdas Hakan Aladag
Department of Mechanical and Industrial Engineering,
University of Toronto, Canada
Department of Statistics, Hacettepe University, Turkey
Advances in Time Series Forecasting
Volume # 2
Editor: Cagdas Hakan Aladag
ISSN (Online): 2543-280X
ISSN (Print): 2543-2796
ISBN (Online): 978-1-68108-528-9
ISBN (Print): 978-1-68108-529-6
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CONTENTS
PREFACE ................................................................................................................................................ i
LIST OF CONTRIBUTORS .................................................................................................................. i(cid:76)(cid:76)
CHAPTER 1 FUZZY TIME SERIES FORECASTING MODELS EVALUATION BASED ON
A NOVEL DISTANCE MEASURE ...................................................................................................... 1
Cagdas Hakan Aladag (cid:68)(cid:81)(cid:71) I. Burhan Turksen
INTRODUCTION .......................................................................................................................... 1
THE PROPOSED DISTANCE MEASURE AND THE SUGGESTED PERFORMANCE
CRITERION ................................................................................................................................... 5
THE APPLICATION ..................................................................................................................... 10
CONCLUDING REMARKS ......................................................................................................... 19
CONFLICT OF INTEREST ......................................................................................................... 21
ACKNOWLEDGEMENTS ........................................................................................................... 21
REFERENCES ............................................................................................................................... 21
CHAPTER 2 A NEW FUZZY TIME SERIES FORECASTING MODEL WITH NEURAL
NETWORK STRUCTURE .................................................................................................................... 24
Eren Bas (cid:68)(cid:81)(cid:71) Erol Egrioglu
INTRODUCTION .......................................................................................................................... 24
PROPOSED METHOD ................................................................................................................. 26
APPLICATION .............................................................................................................................. 30
CONCLUSIONS AND DISCUSSIONS ........................................................................................ 32
CONFLICT OF INTEREST ......................................................................................................... 32
ACKNOWLEDGEMENTS ........................................................................................................... 33
REFERENCES ............................................................................................................................... 33
CHAPTER 3 TWO FACTORS HIGH ORDER NON SINGLETON TYPE-1 AND INTERVAL
TYPE-2 FUZZY SYSTEMS FOR FORECASTING TIME SERIES WITH GENETIC
ALGORITHM ......................................................................................................................................... 37
M.H. Fazel Zarandi, M. Yalinezhaad (cid:68)(cid:81)(cid:71) I.B. Turksen
INTRODUCTION .......................................................................................................................... 37
Interval Type-2 Fuzzy Logic Sets and Systems ...................................................................... 40
Type-2 Fuzzy Logic Sets ........................................................................................................ 40
Non Singleton Interval Type-2 Fuzzy Logic Systems ............................................................ 42
Determination of Footprints of Uncertainty (Umf and Lmf) in Interval Type-2 Fuzzy Logic
Sets .......................................................................................................................................... 43
Fundamental Concepts of Fuzzy Time Series ........................................................................ 45
Proposed Two Factors High Order Non Singletontype-1 and Interval Type-2 Fuzzy Time
Series Systems ........................................................................................................................ 45
Tuning Method for Type-1 and Interval Type-2 FTSs with Genetic Algorithm .................... 48
Experimental Results by Temperature Prediction and TAIEX Forecasting ........................... 50
Temperature Prediction with Proposed Method ........................................................... 50
TAIEX Forecasting By Applying the Proposed Method with Genetic Algorithm ................. 61
GA Procedure .......................................................................................................................... 68
Selection and Pairing .............................................................................................................. 69
Crossover ................................................................................................................................ 69
Mutation and Reinsertion ........................................................................................................ 69
Termination Condition ............................................................................................................ 69
Type Reduction and Defuzzification ...................................................................................... 69
CONCLUSION AND FUTURE WORKS .................................................................................... 73
CONFLICT OF INTEREST ......................................................................................................... 73
ACKNOWLEDGEMENTS ........................................................................................................... 73
REFERENCES ............................................................................................................................... 73
CHAPTER 4 A NEW NEURAL NETWORK MODEL WITH DETERMINISTIC TREND AND
SEASONALITY COMPONENTS FOR TIME SERIES FORECASTING ...................................... 76
Erol Egrioglu, Cagdas Hakan Aladag, Ufuk Yolcu, Eren Bas (cid:68)(cid:81)(cid:71) Ali Z. Dalar
INTRODUCTION .......................................................................................................................... 76
CLASSICAL TIME SERIES FORECASTING MODELS ........................................................ 77
ARTIFICIAL NEURAL NETWORKS FOR FORECASTING TIME SERIES ..................... 80
A NEW ARTIFICIAL NEURAL NETWORK WITH DETERMINISTIC COMPONENTS 85
APPLICATIONS ............................................................................................................................ 89
CONCLUSION ............................................................................................................................... 91
CONFLICT OF INTEREST ......................................................................................................... 91
ACKNOWLEDGEMENTS ........................................................................................................... 92
REFERENCES ............................................................................................................................... 92
CHAPTER 5 A FUZZY TIME SERIES APPROACH BASED ON GENETIC ALGORITHM
WITH SINGLE ANALYSIS PROCESS ............................................................................................... 93
Ozge Cagcag Yolcu
INTRODUCTION .......................................................................................................................... 93
FUZZY TIME SERIES .................................................................................................................. 96
RELATED METHODS .................................................................................................................. 97
Genetic Algorithm (GA) ......................................................................................................... 97
Single Multiplicative Neuron Model ...................................................................................... 98
PROPOSED METHOD ................................................................................................................. 100
APPLICATIONS ............................................................................................................................ 104
CONCLUSION AND DISCUSSION ............................................................................................ 107
CONFLICT OF INTEREST ......................................................................................................... 107
ACKNOWLEDGEMENTS ........................................................................................................... 107
REFERENCES ............................................................................................................................... 107
CHAPTER 6 FORECASTING STOCK EXCHANGES WITH FUZZY TIME SERIES
APPROACH BASED ON MARKOV CHAIN TRANSITION MATRIX ......................................... 111
Cagdas Hakan Aladag (cid:68)(cid:81)(cid:71) Hilal Guney
INTRODUCTION .......................................................................................................................... 111
FUZZY TIME SERIES .................................................................................................................. 113
TSAUR ‘S FUZZY TIME SERIES MARKOV CHAIN MODEL ............................................. 114
THE IMPLEMENTATION ........................................................................................................... 117
CONCLUSION ............................................................................................................................... 124
CONFLICT OF INTEREST ......................................................................................................... 124
ACKNOWLEDGEMENTS ........................................................................................................... 124
REFERENCES ............................................................................................................................... 124
CHAPTER 7 A NEW HIGH ORDER MULTIVARIATE FUZZY TIME SERIES
FORECASTING MODEL ...................................................................................................................... 127
Ufuk Yolcu
INTRODUCTION .......................................................................................................................... 127
RELATED METHODOLOGY ..................................................................................................... 129
The Fuzzy C-Means (FCM) Clustering Method ..................................................................... 129
Single Multiplicative Neuron Model Artificial Neural Network (SMN-ANN) ..................... 130
Fuzzy Time Series ................................................................................................................... 131
THE PROPOSED METHOD ........................................................................................................ 133
APPLICATIONS ............................................................................................................................ 136
CONCLUSIONS AND DISCUSSION .......................................................................................... 140
CONFLICT OF INTEREST ......................................................................................................... 140
ACKNOWLEDGEMENTS ........................................................................................................... 141
REFERENCES ............................................................................................................................... 141
CHAPTER 8 FUZZY FUNCTIONS APPROACH FOR TIME SERIES FORECASTING ......... 144
Ali Z. Dalar, Erol Egrioglu, Ufuk Yolcu (cid:68)(cid:81)(cid:71) Cagdas Hakan Aladag
INTRODUCTION .......................................................................................................................... 144
TYPE-1 FUZZY FUNCTIONS APPROACH .............................................................................. 146
IMPLEMENTATION .................................................................................................................... 148
Australian Beer Consumption Time Series ............................................................................. 148
Turkey Electricity Consumption Time Series ......................................................................... 151
CONCLUSIONS ............................................................................................................................. 153
CONFLICT OF INTEREST ......................................................................................................... 153
ACKNOWLEDGEMENTS ........................................................................................................... 153
REFERENCES ............................................................................................................................... 153
CHAPTER 9 RECURRENT ANFIS FOR TIME SERIES FORECASTING ................................. 156
Busenur Sarıca, Erol Eğrioğlu (cid:68)(cid:81)(cid:71) Barış Aşıkgil
INTRODUCTION .......................................................................................................................... 156
RECURRENT ADAPTIVE NETWORK FUZZY INFERENCE SYSTEMS .......................... 157
APPLICATION .............................................................................................................................. 160
CONCLUSION ............................................................................................................................... 163
CONFLICT OF INTEREST ......................................................................................................... 163
ACKNOWLEDGEMENTS ........................................................................................................... 163
REFERENCES ............................................................................................................................... 163
CHAPTER 10 A HYBRID METHOD FOR FORECASTING OF FUZZY TIME SERIES ......... 165
Eren Bas
INTRODUCTION .......................................................................................................................... 165
THE METHODS USED IN THIS STUDY .................................................................................. 166
Fuzzy Time Series ................................................................................................................... 166
Genetic Algorithm .................................................................................................................. 167
Differential Evolution Algorithm ........................................................................................... 167
PROPOSED METHOD ................................................................................................................. 168
APPLICATION .............................................................................................................................. 171
Analysis of Canadian Lynx Data ............................................................................................ 172
CONCLUSIONS ............................................................................................................................. 173
CONFLICT OF INTEREST ......................................................................................................... 173
ACKNOWLEDGEMENTS ........................................................................................................... 173
REFERENCES ............................................................................................................................... 173
SUBJECT INDEX .................................................................................................................................. (cid:20)(cid:26)(cid:26)
i
PREFACE
Human interest in the future can be traced back to prehistoric times. People have always
wanted to see what can happen in the future. The future is unknown and mysterious. People
have always tried to solve the mystery of the future by using different ways for profit, fame,
power or just curiosity sake. Today forecasting is a multibillion dollar industry. All economic
publications publish many economic forecasting studies; political writers proclaim on
political trends and forthcoming government policies; stockbrokers and financial experts
predict stock market trends, when to buy, and what stocks to choose; and many other
examples can be given which have application to other fields.
Before making plans or making decisions, an estimate must be made of what conditions will
exist over some future period. It is a well-known fact that there is uncertainty about the future.
In order to predict to future by dealing with this uncertainty, forecasting is performed. At the
present time, forecasting is a challenge which has to be overcome in many fields of
application. Forecasting can be considered as a process of using various tools and techniques.
Many methods for forecasting the future have been proposed in the literature over the past
few decades because of the importance of this popular topic. One way to forecast the future is
to use time series analysis. There have been many time series forecasting approaches in the
literature. It is possible to divide these approaches into two subclasses which are conventional
and advanced forecasting methods. Since conventional approaches such as Box-Jenkins
methods has some restrictions such as some assumptions, they cannot always produce reliable
forecasts for real world time series. Furthermore, conventional approaches cannot model
some real world time series because of the specific characteristic of data. Advanced methods
such as neural networks, fuzzy time series, or hybrid approaches have been recently used in
many applications in order to deal with these restrictions arising from conventional methods
and to get more reliable forecasts. Most of the time, these approaches have been competed to
each other. On the other hand, it should be noted that these approaches are complementary
rather than competitive. For example, hybrid approaches are very effective forecasting tools.
And, these approaches sometimes combine conventional and advanced forecasting methods.
The book intends to be a valuable source of recent knowledge about advanced time series
forecasting techniques. New capable advanced forecasting frameworks are discussed and their
applicability is shown. The book includes applications of some powerful recent forecasting
approaches to real world time series. Besides recent advanced forecasting methods, new
efficient forecasting methods are firstly introduced in the book. The readers can find useful
information about advanced time series forecasting, as well as its application to real-life
problems in various domains. I hope the materials covered in this book, provided by the
respectful scholars in the field, motivate and accelerate future progress and introduce new
branches off the time series forecasting.
In Chapter 1, Aladag and Turksen have introduced a new performance measure by defining a
novel distance measure to evaluate forecasting performance of fuzzy time series. Bas and
Egrioglu, in Chapter 2, have suggested a novel fuzzy time series forecasting approach that has
a network structure. In Chapter 3, Zarandi et al. has discussed some Type-1 and Type-2 fuzzy
time series forecasting models. Chapter 4, by Egrioglu et al., introduce a new neural network
model including deterministic trend and seasonality components. In Chapter 5, Yolcu has
presented a fuzzy time series method based on genetic algorithms. Aladag and Guney, in
Chapter 6, have applied a fuzzy time series forecasting model based on Markov chain
transition matrix to stock exchanges. In Cahapter 7, Yolcu has proposed a new high order
multivariate fuzzy time series forecasting model. Chapter 8, by Dalar et al., has discussed a
ii
framework for using fuzzy functions in fuzzy time series forecasting. Sarica et al., in Chapter
9, have introduced Recurrent ANFIS model for time series forecasting. In Chapter 10, Bas has
proposed a hybrid forecasting approach which combines genetic algorithms, differential
evolution algorithms, and fuzzy time series.
The editor would also like to express his sincere thanks to all authors for their valuable
contributions. The editor would also like to acknowledge valuable assistance from Shehzad
Naqvi from Bentham Science Publishers.
Dr. Cagdas Hakan Aladag
Knowledge/Intelligence Systems Laboratory,
Department of Mechanical and Industrial Engineering,
University of Toronto, Toronto,
Canada
Department of Statistics,
Faculty of Science,
Hacettepe University, Ankara,
Turkey