Advances in Time Series Analysis and Forecasting (eBook)

Ignacio Rojas is a full professor at the Department of Computer Architecture and Computer Technology, University of Granada, Spain. Throughout his research career, he has served as a principal investigator or participated in more than 20 research projects obtained in competitive calls including projects of the European Union, the I+D+I Spanish National Government and projects Excellence of the Ministry of Innovation, Science and Enterprise Junta de Andalucía. He has published more than 210 scientific contributions reflected in the database ISI Web of Knowledge, thereof 87 articles in JCR-indexed journals.Héctor Pomares has been a full professor at the University of Granada in Spain since 2001. He has published more than 50 articles in JCR-indexed journals and contributed with more than 150 papers in international conferences. He has led or participated in 15 national projects, one autonomic R&D Excellence project and 13 contracts signed for innovative research through the University of Granada Foundation Company and the Office of Transfer of Research Results. He has made 6 stays longer than one month in prestigious research centers outside of Spain, all of them with a competitive nature. He is a member of the editorial board of the Journal of Applied Mathematics (JCR-indexed) and is the coordinator of the Official Master's Degree in Computer & Network Engineering at the University of Granada.Olga Valenzuela is an Associate Professor at the Department of Applied Mathematics, University of Granada, Spain, where she received her Ph.D. in 2003. She was an invited researcher at the Department of Statistics, University of Jaen, Spain, and at the Department of Computer and Information Science, University of Genova, Italy. Her current research interests include optimization theory and applications, statistical analysis, fuzzy systems, neural networks, time series forecasting using linear and non-linear methods, evolutionary computation and bioinformatics. She has made several stays longer than one month in prestigious research centers outside of Spain, all of them with a competitive nature. She has published more than 67 contributions reflected in the database ISI Web of Knowledge.

Preface 6
Contents 13
Analysis of Irregularly Sampled Time Series: Techniques, Algorithms and Case Studies 16
1 Small Crack Fatigue Growth and Detection Modeling with Uncertainty and Acoustic Emission Application 17
Abstract 17
1 Introduction 18
2 Structure of Models and Likelihood 18
2.1 Crack Propagation Models 19
2.2 Crack Detection Models 20
2.3 Likelihood Function for Bayesian Analysis 21
3 Data Preprocessing 22
3.1 Crack Length Definitions and Correction 22
3.2 Probability of Detection Definitions 23
4 Application Example 24
4.1 Fatigue Life Test Description 24
4.2 Kernel Definition 25
4.3 Measurement Error Analysis 26
4.4 Bayesian Analysis 26
5 Conclusions 30
References 30
2 Acanthuridae and Scarinae: Drivers of the Resilience of a Polynesian Coral Reef 32
Abstract 32
1 Introduction 32
2 Materials and Methods 34
2.1 Study System 34
2.2 Data Sampling 34
2.3 Data Analysis 35
3 Results 36
3.1 Substrate Cover and Species Abundance 36
3.2 Community Structure Variations 36
3.3 Relationship Between Abundance of Acanthuridae and Scarinae and Macroalgae and Turf Cover 38
4 Discussion 40
4.1 Herbivory and Resilience 40
4.2 Comparison with Shifting Systems 41
4.3 Species Richness Increase 41
4.4 Changes in Community Composition 42
4.5 Implication of Different Herbivores 42
5 Conclusion 43
References 43
3 Using Time Series Analysis for Estimating the Time Stamp of a Text 48
Abstract 48
1 Introduction 48
2 Background and Related Work 49
2.1 Language Modeling 49
2.2 Google Books N-Gram Corpus 50
2.3 Related Work 50
3 Implementation Details 52
3.1 Application’s Design 52
3.2 Building Words Time Series 52
3.3 Words’ Fingerprint 53
3.4 Combining the Time Intervals 55
3.5 Optimization 56
4 Case Study and Results 56
5 Conclusions and Further Work 59
Acknowledgements 60
References 60
4 Using LDA and Time Series Analysis for Timestamping Documents 61
Abstract 61
1 Introduction 61
2 Related Work 63
3 Experiment Outline 64
3.1 Corpus Description 64
3.2 Dataset Preprocessing 64
3.3 Training the Topic Model Using LDA 65
3.4 Retrieving of Year Wise Frequency for Keywords 66
3.5 Determining the Document Timestamp and Plotting the Result 67
4 Results Interpretation 71
5 Conclusions and Future Work 72
Acknowledgements 73
References 73
Multi-scale Analysis of Univariate and Multivariate Time Series 74
Fractal Complexity of the Spanish Index IBEX 35 75
1 Introduction 76
2 Fractal Complexity 77
2.1 Fractal Noise 78
2.2 Fractional Brownian Motion 78
2.3 Statistical Tests 82
2.4 Linear Correlations 82
2.5 Conclusions 83
3 ARCH Model 84
References 86
Fractional Brownian Motion in OHLC Crude Oil Prices 87
1 Introduction 87
2 Fractional Brownian Motion 89
2.1 R/S Analysis for Estimation of the Hurst Exponent 89
3 Data and Empirical Results 92
4 Conclusion 96
References 97
Time-Frequency Representations as Phase Space Reconstruction in Symbolic Recurrence Structure Analysis 98
1 Introduction 99
2 Analysis Methods and Data 99
2.1 Symbolic Recurrence Structure Analysis 99
2.2 Phase Space Reconstruction 101
2.3 Complexity Measure 103
2.4 Synthetic Data 104
2.5 Experimental Data 104
3 Results 105
3.1 Synthetic Data 105
3.2 EEG Data 108
4 Discussion 109
References 110
8 Analysis of Climate Dynamics Across a European Transect Using a Multifractal Method 112
Abstract 112
1 Introduction 113
2 Materials and Methods 114
2.1 Study Site and Meteorological Data 114
2.2 MF-DFA Analysis 114
3 Results and Discussion 117
4 Conclusions 122
Acknowledgements 123
References 123
Lineal and Non-linear Time Series Models (ARCH, GARCH, TARCH, EGARCH, FIGARCH, CGARCH etc.) 126
Comparative Analysis of ARMA and GARMA Models in Forecasting 127
1 Introduction 127
2 Estimation of Parameters 129
2.1 Hannan-Rissanen Algorithm (HRA) 130
2.2 Whittle's Estimation (WE) 130
2.3 Maximum Likelihood Estimation (MLE) 130
3 Applications of ARMA and GARMA Modelling to Dow Jones Utilities Index Data Set 131
3.1 First-Order Autoregression (AR(1)) 131
3.2 ARMA(1, 1) 132
3.3 GARMA(1, 1 1, ?)
3.4 GARMA(1, 2 ?, 1)
3.5 Comparison of Performance of ARMA and GARMA Models in Forecasting of Dow Jones Utilities Index Data Set 134
4 Applications of ARMA and GARMA Modelling to Daily Closing Value of the Dow Jones Average 135
4.1 ARMA(1, 1) 136
4.2 GARMA(1, 2 ?, 1)
5 Applications of ARMA and GARMA Modelling to Daily Total Return of the Dow Jones Utility Average 137
5.1 ARMA(1, 1) 138
5.2 GARMA(1, 2 ?, 1)
6 Conclusion 139
References 139
10 SARMA Time Series for Microscopic Electrical Load Modeling 141
Abstract 141
1 Introduction 141
2 Seasonal ARMA Load Modeling 143
2.1 Seasonality Considerations 143
2.2 Stationarity Considerations 145
2.3 SARIMA Approach 145
3 Methodology 146
3.1 Normalization 146
3.2 Identification and Adjustment of SARIMA Models 147
3.3 Simulation and De-normalization 148
4 Analysis 148
4.1 Model Observation 148
4.2 Qualitative Analysis 149
4.3 Application Example 150
5 Prospects 151
6 Conclusion 152
Acknowledgements 152
References 152
Diagnostic Checks in Multiple Time Series Modelling 154
1 Introduction 154
2 Definitions and Assumptions 155
3 Preliminaries 156
4 Application in Diagnostic Checking 157
5 Examples of VARMA(p, q) models 159
6 Conclusions 163
References 165
Mixed AR(1) Time Series Models with Marginals Having Approximated Beta Distribution 166
1 Introduction and Preliminaries 166
2 The ABp, qAR(1) Model with Parent mathfrakM1 169
3 The ABAR(1) Model with Parent mathfrakM2 172
4 Generalized Beta as the Parent Distribution 175
References 177
Prediction of Noisy ARIMA Time Series via Butterworth Digital Filter 179
1 Introduction 179
2 Noise Reduction Techniques 180
2.1 The Proposed ARIMA-? Procedure 181
2.2 The Underlying Stochastic Process and the Noise Model 183
2.3 The ARIMA-BW Filter Unified Framework 184
2.4 The Algorithm 186
3 Empirical Experiment 187
3.1 Simulated Time Series 190
3.2 Real Time Series 195
3.3 Results 196
3.4 Concluding Remarks and Future Work 201
References 201
Mandelbrot's 1/f Fractional Renewal Models of 1963--67: The Non-ergodic Missing Link Between Change Points and Long Range Dependence 203
1 Ergodic and Non-ergodic Solutions to the Paradoxes of 1/f Noise and Long Range Dependence 204
2 fGn and the Fractional Renewal Process Compared 206
3 Mandelbrot's Fractional Renewal Route to 1/f 207
4 The Hurst Effect Versus 1/f Versus LRD 209
4.1 The Hurst Effect 210
4.2 1/f Spectra 211
4.3 LRD 212
5 Conclusions 212
References 213
Detection of Outlier in Time Series Count Data 215
1 Introduction 215
2 GARMA Models 217
2.1 Poisson GARMA Models with an Outlier 218
3 Estimation 218
4 Model Inference---Outlier Detection 221
4.1 Determination of t0 and LR Test 221
5 Application 222
6 Conclusions 226
References 226
Ratio Tests of a Change in Panel Means with Small Fixed Panel Size 228
1 Introduction 228
1.1 State of Art 229
1.2 Motivation 229
1.3 Structure of the Paper 229
2 Panel Change Point Model 230
3 Test Statistics and Asymptotic Results 231
4 Estimation of the Correlation Structure 233
5 Simulation Study 234
6 Real Data Analysis 239
7 Conclusions 240
7.1 Discussion 241
References 245
Advanced Time Series Forecasting Methods 246
17 Operational Turbidity Forecast Using Both Recurrent and Feed-Forward Based Multilayer Perceptrons 247
Abstract 247
1 Introduction 248
2 Estimating Turbidity by Machine Learning 248
2.1 Definition of the Turbidity 248
2.2 State of the Art 249
2.3 Turbidity, Uncertainty and Water Production 249
3 Design of the Model 249
3.1 Multilayer Perceptron 249
3.2 Specific Architectures 250
3.3 Bias Variance and Regularization Methods 252
3.4 Model Selection 252
3.5 Quality Criteria 253
4 Site of Study: Yport Pumping Well 253
4.1 Overview of the Basin 253
4.2 Database 255
5 Results 255
5.1 Selected Architecture 255
6 Conclusion 259
Acknowledgements 259
References 259
18 Productivity Convergence Across US States in the Public Sector. An Empirical Study 261
Abstract 261
1 Introduction 261
2 Existing Research 262
3 Data and Methodology 263
3.1 Data 263
3.2 Methodology and Models 264
4 Results 266
4.1 Explanatory Analysis of Outputs 266
4.2 Productivity Analysis Across US States 268
4.3 Convergence Analysis 269
5 Discussion and Conclusions 272
6 Limitations and Future Research 273
Acknowledgements 273
References 273
Proposal of a New Similarity Measure Based on Delay Embedding for Time Series Classification 275
1 Introduction 275
2 Time Series Classification and Similarity Measures 277
2.1 Approaches for Time Series Classification 277
2.2 Time Series Similarity Measures 278
3 Proposal for a New Similarity Measure 280
3.1 Cross Translation Error: CTE 280
3.2 Dynamic Translational Error DTE 282
4 Simulation Study 282
4.1 Data Set Used 283
4.2 Simulation Results 283
5 Conclusion 286
References 287
A Fuzzy Time Series Model with Customized Membership Functions 289
1 Introduction 289
2 The Methodology 290
2.1 Data Normalization 291
2.2 Fuzzy C-Means Clustering of Input Vectors 291
2.3 Forming Fuzzy Rules 292
2.4 Membership Functions of the Fuzzy Rule Consequents 293
2.5 The Fuzzy Inference and Optimization of System Outputs 294
3 Modeling and Forecasting 296
3.1 The Impact of Model Parameters 297
4 A Practical Application 299
5 Conclusions 301
References 301
Model-Independent Analytic Nonlinear Blind Source Separation 303
1 Introduction 303
2 Method 306
3 Experiments 311
4 Conclusion 314
References 314
Dantzig-Selector Radial Basis Function Learning with Nonconvex Refinement 316
1 Introduction 316
2 The Radial Basis Function Optimization Problem 319
2.1 Dantzig-Selector Optimization for Model Order Selection 320
3 The Prediction of Chaotic Time-Series 321
4 Gradient Computation of Skew RBF 326
5 Background and Related Work 328
6 Conclusions and Future Work 328
References 329
A Soft Computational Approach to Long Term Forecasting of Failure Rate Curves 331
1 Introduction 331
2 The Modeling and Forecasting Methodology 333
2.1 The Model Function 334
2.2 Standardizing the Failure Rate Curve Models 336
2.3 Identifying Typical Standardized Failure Rate Curve Models 337
2.4 Predicting Failure Rate Curves of Active Products 337
3 A Case Study 339
3.1 The Typical Standardized Failure Rate Curve Models of a Commodity 339
3.2 Results and Comparisons 340
4 Conclusions 342
References 343
24 A Software Architecture for Enabling Statistical Learning on Big Data 345
Abstract 345
1 Introduction 345
1.1 What is Big Data? 346
1.2 Big Data Analytics Process Model 346
1.3 Overview of this Paper 348
2 Big Data Analytics 348
2.1 Analysis Techniques and Tools 348
2.2 Challenge 351
3 Proposed Model-Driven Architecture (MDE) 352
3.1 General Principles 352
3.2 Overview of Proposed Architecture 352
3.3 Current Implementation 353
3.4 Commodity Pricing Case Study 354
4 Conclusion 357
Applications in Time Series Analysis and Forecasting 360
Wind Speed Forecasting for a Large-Scale Measurement Network and Numerical Weather Modeling 361
1 Introduction 361
2 Data 362
3 Behavior of the Raw NWP Predictor 363
4 Statistical Modeling for NWP Calibration 365
4.1 Linear Models 365
4.2 Semiparametric Models 367
5 Conclusions 371
References 372
Analysis of Time-Series Eye-Tracking Data to Classify and Quantify Reading Ability 374
1 Introduction 375
2 Previous Works and Proposed Idea 376
3 Experimental Setup 377
3.1 Peripheral Vision and Reading Speed 378
4 Experimental Results 378
5 Analysis of Data 379
6 Conclusion 384
References 384
Forecasting the Start and End of Pollen Season in Madrid 386
1 Introduction 386
2 Data Description 387
3 Definition of Season Start and End 388
4 Methods 390
4.1 Feature Generation 390
4.2 Setting up the Data 392
4.3 Feature Selection 393
4.4 Computational Intelligence Models 393
5 Results 394
6 Conclusions and Future Works 397
References 397
28 Statistical Models and Granular Soft RBF Neural Network for Malaysia KLCI Price Index Prediction 399
Abstract 399
1 Introduction 399
2 Statistical Models 400
2.1 Box-Jenkins Time Series-Class Models 400
2.2 Asymmetric ARCH-GARCH Class Models for Financial Data 401
3 Neural Networks 402
3.1 Mathematical Model of Neural Network 402
3.2 RBF Neural Networks 403
4 Building the Statistical and G RBF NN Prediction Models 406
5 Empirical Comparison and Conclusion 409
Acknowledgements 409
References 410
Author Index 411