Applied Time Series Analysis and Innovative Computing (eBook)

Applied Time Series Analysis and Innovative Computing 2
Chapter 1 14
Introduction 14
1.1 Applied Time Series Analysis 15
1.1.1 Basic Definitions 15
1.1.2 Basic Applied Time Series Models 15
1.1.3 Frequency Domain Models 15
1.2 Advances in Innovative Computing Paradigms 16
1.2.1 Computing Algorithms and Databases 16
1.2.2 Integration of Hardware, Systems and Networks 16
1.2.3 Internet, Web and Grid Computing 17
1.2.4 Visualization, Design and Communication 17
1.3 Real-World Applications: Innovative Computing Paradigms for Time Series Problems 18
1.3.1 Developing Innovative Computing Algorithms for Business Time Series 18
1.3.2 Developing Innovative Computing Algorithms for Biological Time Series 19
1.3.3 Developing Innovative Computing Algorithms for Astronomical Time Series 19
Chapter 2 21
Applied Time Series Analysis 21
2.1 Basic Characteristics of Time Series 22
2.1.1 Estimation of Correlation 22
2.1.1.1 Auto-Correlation Analysis 22
2.1.1.2 Cross-Correlation Analysis 22
2.1.1.3 Autocorrelation Functions 23
2.1.2 Stationary Time Series 24
2.1.3 Smoothing of the Time Series 24
2.1.4 Periodogram Analysis 25
2.2 Autoregression and ARIMA Models 26
2.2.1 Time Series Regression 26
2.2.2 Autoregressive Moving Average Models 26
2.2.3 Building ARIMA Models 27
2.2.4 Forecasting and Evaluation 28
2.2.5 Causality of the Time Series 28
2.3 Mathematical Models in the Frequency Domain 29
2.3.1 Introduction 29
2.3.2 Discrimination Analysis 30
2.3.3 Clustering Analysis 31
2.3.4 Principal Components and Factor Analysis 33
2.3.5 Dynamic Fourier Analysis 34
2.3.6 Random Coefficient Regression 35
2.3.7 Discrete Fourier Transform 36
Chapter 3 37
Advances in Innovative Computing Paradigms 37
3.1 Research Advances in Computing Algorithms and Databases 37
3.1.1 Knowledge Extraction Methods 37
3.1.2 Exploiting Large Complex Databases 38
3.1.3 Neural Computing Algorithms 38
3.1.4 Fuzzy Computing Algorithms 39
3.1.5 Evolutionary Computing Algorithms 39
3.1.6 Quantum Computing Algorithms 40
3.1.7 Swarm-Based Computing Algorithms 40
3.1.8 DNA Computing Algorithms 41
3.1.9 Theoretical Modeling and Simulations 41
3.2 Research Advances in Integration of Hardware, Systems and Networks 41
3.2.1 Innovative Experimental Hardware System 41
3.2.2 Data-Acquisition Devices 42
3.2.3 Interaction Devices for Visual Exploration 42
3.2.4 Graphics Processing Units and Co-Processors for Innovative Computing 43
3.2.5 Networking and Interoperability 43
3.2.6 Code Optimization and Integration 44
3.3 Research Advances in Internet, Web and Grid Computing 44
3.3.1 Distributed Computation and Data Sharing 44
3.3.2 Large-Scale Collaborations over the Internet 44
3.3.3 Grid Computing 45
3.3.4 Pooling of Remote Computer Resources 45
3.3.5 Integration of Knowledge Metadata Systems 45
3.4 Research Advances in Visualization, Design and Communication 46
3.4.1 Novel Solutions to Visualization and Communication Challenges 46
3.4.2 Displaying of Complex Information 46
3.4.3 Escaping Flatland 47
3.4.4 Systems Integration for High Performance Image Processing 47
3.4.5 Representation of Uncertainties 48
3.4.6 Informative Graphics for Scientific Communication 48
3.5 Advances and Applications for Time Series Problems 49
3.5.1 Efficient Retrieval of Similar Time Series 49
3.5.2 Automatic Classification of Time Series Sequences 49
3.5.3 Time Warping Algorithms 50
3.5.4 Time Frequency Clustering of Time Series Datasets 52
3.5.5 Enhanced Representation for Complex Time Series 52
3.5.6 Automatic Monitoring of Large and Complex Time Series 53
3.6 An Illustrative Example of Building an Innovative Computing Algorithm for Simulated Time Series 53
3.6.1 Description of the Simulated Time Series Problem 53
3.6.2 Background of the Methodology 54
3.6.3 Building the Innovative Regression Model 56
3.6.3.1 Neural Network Regression Models 56
3.6.3.2 Fuzzy Clustering 58
3.6.3.3 Hybrid Neural Network and Fuzzy Clustering (NN-FC) 59
3.6.4 Experimental Results with the Simulated Time Series 60
3.6.5 Discussions and Further Works 62
Chapter 4 63
Real-Word Application I: Developing Innovative Computing Algorithms for Business Time Series 63
4.1 Business Time Series 63
4.2 Advances in Business Forecasting 64
4.2.1 Basic Econometrics Models 64
4.2.2 Neural Computing Models 64
4.2.3 Evolutionary Computing Models 65
4.2.4 Hybrid Intelligent Models 65
4.3 Developing a Hybrid Intelligent Econometrics Model for Business Forecasting 66
4.3.1 Vector Autoregression 66
4.3.2 Neural Network 67
4.3.3 Genetic Algorithm 70
4.3.4 A Cybernetic Framework of Hybrid Vector Autoregression, Neural Network and Genetic Algorithm 72
4.4 Application for Tourism Demand Forecasting 73
4.4.1 Quantifying Cross-Market Dynamics 74
4.4.2 Experimental Results 74
4.5 Application for Cross-Market Financial Forecasting 75
4.5.1 Quantifying the Cybernetic Lead–Lag Dynamics across Different Markets 76
4.5.2 Benchmark Stand-Alone Neural Network 76
4.5.3 Hybrid Innovative System and Results Comparison 77
4.6 Discussions and Further Works 78
Chapter 5 79
Real-Word Application II: Developing Innovative Computing Algorithms for Biological Time Series 79
5.1 Biological Time Series 79
5.2 Advances in Experimental Designs for Microarray Time Series 80
5.2.1 Microarray Experiments 80
5.2.2 Microarray Time Series and Applications 81
5.3 Reverse Engineering of Biological Networks 82
5.3.1 Introduction 82
5.3.2 Materials and Methods 83
5.3.2.1 Elman Neural Networks 83
5.3.2.2 Support Vector Machines 85
5.3.2.3 Ensemble of Innovative Models 87
5.3.2.4 Pedagogical Rule Extraction for Biological Network Inference 88
5.4 Models for Biological Network Inference 90
5.4.1 Biological Time Series Datasets 90
5.4.2 Analysis with Simulated Non-stationary Datasets 91
5.4.3 Analysis with Real Biological Datasets 91
5.4.4 Rule Extraction for Reverse Engineering of Biological Networks 92
5.5 Discussions and Further Works 93
Chapter 6 95
Real-Word Application III: Developing Innovative Computing Algorithms for Astronomical Time Series 95
6.1 Astronomical Time Series 95
6.2 Advances and Applications of Innovative Computing Paradigms 96
6.2.1 Classification of Astronomical Time Series 96
6.2.2 Clustering of Astronomical Time Series 96
6.2.3 Semi-Supervised Learning for Astronomical Time Series 97
6.2.4 Anomaly Detection of Astronomical Time Series 98
6.3 Motivations for Investigating the Quasar Time Series with Innovative Approaches 98
6.4 Advances in Emerging Methods for Quasar Studies 99
6.4.1 Variability Properties of the Quasar Light Curves 99
6.4.2 Algorithms Based on Variability and Proper Motion for Quasar Classification 101
6.4.2.1 Data: Deviation from a Constant Brightness Lightcurve 102
6.4.2.2 First Criterion: Selection on Photometry: Magnitude and Colour 103
6.4.2.3 Second Criterion: The Slope of Variograms 103
6.4.2.4 Third Criterion: QSO and Be Star Colors 104
6.4.2.5 Fourth Criterion: Manual Selection 104
6.4.2.6 Follow-Up Spectroscopy Experiments and Works 104
6.4.3 Bayesian Classification for Efficient Photometric Selection of Quasars 105
6.4.3.1 Follow-Up Works to This Automatic Photometric Selection of Quasars 106
6.4.3.2 Nonparametric Bayesian Classification (NBC) 107
6.4.3.3 Fast Algorithms for Computing the Kernel Density Estimate 107
6.4.4 Machine Learning Paradigms for Quasar Selection 109
Bibliography 110

"Chapter 1 Introduction (p. 1-2)

Abstract This book is organized as follows. In first two sections of this chapter, it is the brief introduction to the applied time series analysis and the advances in innovative computing paradigms. In the third section, we describe briefly about the three real-world applications of innovative computing paradigms for time series problems. The contributions of these algorithms to the time series analysis are also described briefly in that section and in more details in their respective chapters. In Chap. 2, we describe about the applied time series analysis generally. Time series analysis models including time domain models and frequency domain models are covered. In Chap. 3, we describe about the recent advances in innovative computing paradigms.

Topics like computing algorithms and databases, integration of hardware, systems and networks, Internet and grid computing, and visualization, design and communication, will be covered. The advances of innovative computing for time series problems are also discussed, and an example of building of an innovative computing algorithm for some simulated time series is illustrated. In Chap. 4, we present the real-world application of innovative computing paradigms for time series problems.

The interdisciplinary innovative computing techniques are applied to understand, model and design systems for business forecasting. In Chap. 5, the second real-world application is for the analysis of the biological time series. Recurrent Elman neural networks and support vector machines have been outlined for temporal modeling of microarray continuous time series data sets. In Chap. 6, we present the last real-world application for the astronomical time series. It is to explore if some innovative computing algorithms can automatically classify the light curves of the quasars against the very similar light curves of the other stars.

1.1 Applied Time Series Analysis

1.1.1 Basic Definitions

A time series can be regarded as any series of measurements taken at different times. Different from other common data analysis problems, time series data have a natural temporal ordering. Examples of time series are the daily stock prices, daily temperature, temporal gene expression values, and temporal light intensity of astronomical objects etc. Applied time series analysis consists of empirical models for analyzing time series in order to extract meaningful statistics and other properties of the time series data. Time series models usually take advantage of the fact that observations close together in time are generally more closely related than observations further apart.

There are many reasons to analyze the time series data, for example, to understand the underlying generating mechanism better, to achieve optimal control of the system, or to obtain better forecasting of future values. Time series forecasting is about the employment of time series model to forecast future events based on past events. The forecasting methods have been applied in various domains, like for example, business forecasting (Ao 2003b–e, 2006, 2007b) and genomic analysis (Ao et al. 2004, Ao 2006, 2007a).

1.1.2 Basic Applied Time Series Models

Time series models have various forms and represent different stochastic processes. Different from a deterministic process, in a stochastic process, there is some indeterminacy in its future evolution described by probability distributions. Time series analysis model is usually classified as either time domain model or frequency domain model. Time domain models include the auto-correlation and cross-correlation analysis.

In a time domain model, mathematical functions are usually used to study the data with respect to time. The three broad classes for modeling the variations of time series process are the autoregressive (AR) models, the integrated (I) models, and the moving average (MA) models. They all depend linearly on previous time series data points (Box and Jenkins 1976). The autoregressive fractionally integrated moving average (ARFIMA) model is the generalization of these three classes."