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 tenders, including projects of the European Union, the I+D+I Spanish National Government and the Unit of Excellence of the Ministry of Innovation, Science and Enterprise Junta de Andalucía. He has published more than 250 scientific contributions reflected in Web of Science, including 145 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 over 150 papers at international conferences. He has led or participated in 15 national projects, one autonomic R&D Excellence project and 13 contracts for innovative research through the University of Granada Foundation Company and the Office of Transfer of Research Results. He has been a visitor at numerous prestigious research centers outside Spain. 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 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 been a visitor at numerous prestigious research centers outside Spain. She has published more than 72 papers reflected in Web of Science.

Preface 6
Contents 12
Advanced Mathematical Methodologies in Time Series 15
Forecasting via Fokker–Planck Using Conditional Probabilities 16
1 Introduction 16
2 Fokker–Planck Solution Versus mathcalN(µ, e) 17
3 Definition of the Past Values of Parameter b 18
4 Method for One-Step Ahead Forecasts 19
5 Results for One-Step Ahead Forecasts 20
6 Method for Two-Step Ahead Forecasts 21
7 Results for Two-Step Ahead Forecasts 22
8 Conclusion 24
References 26
Cryptanalysis of a Random Number Generator Based on a Chaotic Ring Oscillator 27
1 Introduction 27
2 Target System 28
3 Attack System 31
4 Numerical Results 32
5 Conclusions 35
References 36
Further Results on a Robust Multivariate Time Series Analysis in Nonlinear Models with Autoregressive and t-Distributed Errors 37
1 Introduction 38
2 The Observation Model 40
3 Generalized EM Algorithm 42
EM Algorithm for Estimating Unknown Parameters 42
Bootstrapping Algorithm for Determining the Covariance Matrix 43
4 Field Experiment Setup and Its Results 45
5 Conclusions and Outlook 49
References 49
A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations 51
1 Introduction 52
2 Estimation of the Model Parameters 53
Modified Maximum Likelihood Estimators 53
Least Squares Estimators 55
Adaptive Modified Maximum Likelihood Estimators 55
3 Efficiency and Robustness Comparisons of the Estimators 56
4 Significance Test of the Model 63
5 Generalization to AR(q) Model 73
6 Conclusion 74
References 74
Prediction of High-Dimensional Time Series with Exogenous Variables Using Generalized Koopman Operator Framework in Reproducing Kernel Hilbert Space 76
1 Introduction 77
2 Theory 78
Koopman Operator of Dynamical System and Its Generalization to Systems with Input 78
Reproducing Kernel Hilbert Space and Gaussian Processes Regression 81
Koopman Operator in Reproducing Kernel Hilbert Space 83
3 Numerical Algorithm 86
4 Numerical Examples and Applications 86
5 Conclusion and Outlook 87
References 88
Eigenvalues Distribution Limit of Covariance Matrices with AR Processes Entries 89
1 Introduction 89
2 Main Result 91
3 Numerical Simulations 93
4 Proof of the Main Result 95
Proof of the Theorem 1 97
References 101
Computational Intelligence Methods for Time Series 102
Deep Learning for Detection of BGP Anomalies 103
1 Introduction 103
2 ANN—Deep Learning 105
3 Anomalous Events 107
BGP Datasets 107
Routing Table Leak Events 110
Worm Events 113
Power Outage Events 114
4 Classification of Anomalous Events 115
Methodology 115
Performance Measures 116
Classification Results 118
5 Conclusion 119
References 119
Using Scaling Methods to Improve Support Vector Regression's Performance for Travel Time and Traffic Volume Predictions 122
1 Introduction 122
2 Data and Work Objectives 123
3 Related Work 124
4 Methods 125
Support Vector Regression 125
Scaling Methods 126
Error Measurements and Validation Method 127
5 Travel Time Prediction 127
6 Traffic Volume Prediction 129
7 Generalisation 130
8 Conclusion 133
References 133
Dimensionality Reduction and Similarity Measures in Time Series 135
Linear Trend Filtering via Adaptive LASSO 136
1 Introduction 136
2 Adaptive LASSO in Trend Filtering 139
Computational Aspects 142
3 Theoretical Properties 143
4 Simulations 144
5 Conclusion 148
References 149
An Efficient Anomaly Detection in Quasi-Periodic Time Series Data—A Case Study with ECG 151
1 Introduction 152
Definition of Time Series Discords 152
Related Works 153
2 Proposed Idea—Mother Signal 154
What Is Mother Signal? 154
Creation of the Mother Signal 155
3 Proposed Algorithm, Experimental Data, and Results 157
4 Experimental Data and Results 157
5 Conclusion 160
References 160
Similarity Analysis of Time Interval Data Sets—A Graph Theory Approach 162
1 Introduction and Motivation 162
2 Related Work 163
3 Similarities Between Time Intervals 165
Geometrical Analysis 166
Metadata and Dealing with Deadlines 167
Similarity of Two Time Intervals 167
4 Similarity Analysis Regarding Time Interval Data Sets 168
Dynamic Changes Within One Data Set 169
How to Deal with Different Cardinality 171
5 Discussion and Outlook 172
6 Conclusion 172
References 173
Logical Comparison Measures in Classification of Data—Nonmetric Measures 175
1 Introduction 175
2 Logical Comparison Measures 176
T-norms and T-conorms as the Measures for Comparison 178
3 Classification 181
Description of the Similarity Based Classifiers 181
Data Sets 182
4 Results 184
5 Conclusions 184
References 185
Econometric Models 187
Asymptotic and Bootstrap Tests for a Change in Autoregression Omitting Variability Estimation 188
1 Introduction and Main Goals 188
2 Autoregressive Model with Possibly Changed Parameter 189
3 Test Statistic for Change in Autoregression 190
4 Asymptotic Critical Values 191
5 Bootstrap Test Procedure 192
6 Simulation Study 193
7 Application to Stock Exchange Index 196
8 Conclusions 199
References 203
Distance Between VARMA Models and Its Application to Spatial Differences Analysis in the Relationship GDP—Unemployment Growth Rate in Europe 204
1 Introduction 204
2 A Distance Measure Between VARMA Models 205
Univariate Models Implied by a VARMA Model 205
The Proposed Distance 206
Distance Estimation Procedure 210
3 Spatial Variability of the Relationship Between Unemployment and GDP 210
4 Conclusions 215
References 216
Copulas for Modeling the Relationship Between Inflation and the Exchange Rate 217
1 Introduction 218
2 Methodology and Theoretical Background 218
3 Results and Discussion 222
4 Conclusion 227
References 228
Energy Time Series Forecasting 229
Fuel Consumption Estimation for Climbing Phase 230
1 Introduction 230
2 Fuel Consumption Statistical Analysis 232
3 Fuel Consumption Influencing Factors 233
4 Improved Model Algorithm 234
Basic Procedures and Ideas 234
GA-BP-AdaBoost Parameters Setup 234
5 Model Validations 237
Model Feasibility Evaluation Criteria 237
Model Testing and Evaluation 237
Model Testing and Evaluation 239
6 Conclusion 241
References 241
Time Series Optimization for Energy Prediction in Wi-Fi Infrastructures 243
1 Introduction 243
2 System Identification of Time Series 244
3 Energy Prediction in Access Points 245
Prediction Approach 245
Energy Data 246
Prediction Results 247
4 Parameter Tuning for Improving the Accuracy 249
Direct Search 249
Metaheuristics for Efficient Search 251
5 Conclusions 253
References 254
An Econometric Analysis of the Merit-Order Effect in Electricity Spot Price: The Germany Case 256
1 Introduction 256
2 The Merit-Order Effect 258
3 Empirical Evidence 260
Data 260
Empirical Methodology: ARMA-X-GARCH-X Model 263
4 Conclusion 267
References 267
Forecasting in Real Problems 269
The Analysis of Variability of Short Data Sets Based on Mahalanobis Distance Calculation and Surrogate Time Series Testing 270
1 Introduction 271
2 Data and Methods of Analysis 272
3 Results and Discussion 274
4 Summary 281
References 281
On Generalized Additive Models with Dependent Time Series Covariates 283
1 Introduction 284
2 The GAM-PCA-VAR Model 285
3 Theoretical Results 290
4 Simulation Study 294
5 Application to Air Pollution Data 296
6 Conclusions 300
References 301
A Bayesian Approach to Astronomical Time Delay Estimations 303
1 Introduction 303
2 Accretion onto Black Holes and Importance of Time Delay Estimations 305
3 Our Bayesian Approach and Its Application 306
A Bayesian State–Space Model for Time Delay Estimations 306
Application to Observational Data 308
4 Discussion 310
Applicability of Our Method for Other Astronomical Systems 310
Advantages of Our Method and Future Work 312
Diversity of Light Curves in Astronomy 313
5 Conclusions 314
References 314
Further Results on a Modified EM Algorithm for Parameter Estimation in Linear Models with Time-Dependent Autoregressive and t-Distributed Errors 316
1 Introduction 316
2 The Observation Model 318
3 The Modified EM Algorithm 320
4 An Application to Vibration Analysis 323
5 Summary, Conclusions, and Outlook 328
References 328
Author Index 331