Introduction to time series modeling with applications in R:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Boca Raton ; London ; New York
CRC Press
2021
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| Edition: | Second edition |
| Series: | Monographs on Statistics and Applied Probability
166 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xvi, 323 Seiten Diagramme |
| ISBN: | 9780367494247 9780367187330 |
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| adam_text | Contents Preface Preface for Second Edition xi xiii R and the Time Series Modeling Package TSSS xv 1 Introduction and Preparatory Analysis 1.1 Time Series Data 1.2 Classification of Time Series 1.3 Objectives of Time Series Analysis 1.4 Pre-Processing of Time Series 1.4.1 Transformation of variables 1.4.2 Differencing 1.4.3 Month-to-month basisand year-over-year 1.4.4 Moving average 1.5 Organization of This Book 1 1 6 9 9 10 11 12 14 17 2 The Covariance Function 2.1 The Distribution of Time Series and Stationarity 2.2 The Autocovariance Function of Stationary Time Series 2.3 Estimation of the Autocovariance and Autocorrelation Functions 2.4 Multivariate Time Series and Scatterplots 2.5 Cross-Covariance Function and Cross-Correlation Function 19 19 22 The Power Spectrum and the Periodogram 3.1 The Power Spectrum 3.2 The Periodogram 3.3 Averaging and Smoothing of the Periodogram 35 35 40 44 3 23 26 29
vi CONTENTS 3.4 3.5 Computational Method of Periodogram Computation of the Periodogram by Fast Fourier Transform 48 Statistical Modeling 4.1 Probability Distributions and Statistical Models 4.2 К-L Information and Entropy Maximization Principle 4.3 Estimation of the К-L Information and the Log-Likelihood 4.4 Estimation of Parameters by the Maximum Likelihood Method 4.5 AIC (Akaiké Information Criterion) 4.5.1 Eva!uation of C 4.5.2 Evaluation of C3 4.5.3 Evaluation of C2 4.5.4 Evaluationof C and AIC 4.6 Transformation of Data 55 55 60 The Least Squares Method 5.1 Regression Models and the Least Squares Method 5.2 The Least Squares Method Based on the Householder Transformation 5.3 Selection of Order by AIC 5.4 Addition of Data and Successive Householder Reduction 5.5 Variable Selection by AIC 79 79 6 Analysis of Time Series Using ARMA Models 6.1 ARMA Model 6.2 The Impulse Response Function 6.3 The Autocovariance Function 6.4 The Relation Between AR Coefficientsand PARCOR 6.5 The Power Spectrum of the ARMAProcess 6.6 The Characteristic Equation 6.7 The Multivariate AR Model 91 91 92 94 96 96 100 104 7 Estimation of an AR Model 7.1 Fitting an AR Model 7.2 Yule-Walker Methodand Levinson’s Algorithm 7.3 Estimation of an AR Model by the Least Squares Method 113 113 115 4 5 49 64 65 69 71 72 72 73 73 81 83 87 88 116
CONTHNTS 7.4 7.5 7.6 Hstimation of an AR Model by the PARCt )RMethod Large Sample Distribution of the Estimates Hstimation of Multivariate AR Model by the Yule-Walker Method Hstimation of Multivariate AR Model by the Least Squares Method 11H 121 The Locally Stationary AR Model 8.1 Locally Stationary AR Model 8.2 Automatic Partitioning of the Time Interval into an Arbitrary Number of Subintervals 8.3 Precise Hstimation of the Change Point 8.4 Posterior Probability of the Change Point 137 137 Analysis of Time Series with a State-Space Model 9.1 The State-Space Model 9.2 State Hstimation via the Kalman Hilter 9..3 Smoothing Algorithms 9.4 Long-Term Prediction of the Stale 9.5 Prediction of Time Series 9.6 Likelihood Computation and Parameter Hstimation for Time Series Models 9.7 Interpolation of Missing Observations 153 153 156 158 158 159 7.7 8 9 Vįį 124 ] 2у 139 144 149 163 166 10 Estimation of the ARMA Model 10.1 State-Space Representation of the ARMA Model 10.2 Initial State Distribution for an AR Model 10.3 Initial State Distribution of an ARMA Model 10.4 Maximum Likelihood Hstimates of an ARMAModel 10.5 Initial Hstimates of Parameters 171 171 172 174 175 178 11 Estimation of Trends 11.1 The Polynomial Trend Model 11.2 Trend Component Model - Model for GradualChanges 11.3 Trend Model 181 181 184 188 12 The Seasonal Adjustment Model 12.1 Seasonal Component Model 12.2 Standard Seasonal Adjustment Model 12.3 Decomposition Including a Stationary AR Component 12.4 Decomposition Including a Trading-Day Effect 195 195 198 201 206
viii CONTENTS 13 Time-Varying Coefficient AR Model 13.1 13.2 13.3 13.4 Time-Varying Variance Model Time-Varying Coefficient AR Model Estimation of the Time-Varying Spectrum The Assumption on System Noise for the Time-Varying Coefficient AR Model 13.5 Abrupt Changes of Coefficients 14 Non-Gaussian State-Space Model 14.1 14.2 14.3 14.4 14.5 Necessity of Non-Gaussian Models Non-Gaussian State-Space Models and State Estimation Numerical Computation of the State Estimation Fonnula Non-Gaussian Trend Model Non-symmetric Distribution ֊ A Time-Varying Variance Model 14.6 Applications of the Non-Gaussian State-Space Model 14.6.1 Processing of the outliers by a mixture of Gaussian distributions 14.6.2 A nonstationary discrete process 14.6.3 A direct method of estimating the time-varying variance 14.6.4 Nonlinear state-space models 15 Particle Filter 15.1 The Nonlinear Non-Gaussian State-Space Model and Approximations of Distributions 15.2 Particle Filter 15.2.1 One-step-ahead prediction 15.2.2 Filtering 15.2.3 Algorithm for the particle filter 15.2.4 Likelihood of a model 15.2.5 On the re-sampling method 15.2.6 Numerical examples 15.3 Particle Smoothing Method 15.4 Nonlinear Smoothing 16 Simulation 16.1 Generation of Uniform Random Numbers 16.2 Generation of White Noise 16.2.1 χ1 distribution 16.2.2 Cauchy distribution 16.2.3 Arbitrary distribution 213 213 217 222 224 225 229 229 230 232 235 240 244 245 245 246 247 249 249 263 253 253 254 254 255 256 259 262 267 267 269 272 272 272
CONTENTS 16.3 Simulation of ARMA models 16.4 Simulation Using a State-Space Model 16.5 Simulation with the Non-Gaussian State-Space Model ix 273 275 279 A Algorithms for Nonlinear Optimization 283 В Derivation of Levinson’s Algorithm 285 C Derivation of the Kalman Filter and Smoother Algorithms C.l Kalman Filter C.2 Smoothing 289 289 290 D Algorithm for the Particle Filter D.l One-Step-Ahead Prediction D.2 Filter D.3 Smoothing 293 293 294 295 Bibliography 311 Index 319
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| adam_txt |
Contents Preface Preface for Second Edition xi xiii R and the Time Series Modeling Package TSSS xv 1 Introduction and Preparatory Analysis 1.1 Time Series Data 1.2 Classification of Time Series 1.3 Objectives of Time Series Analysis 1.4 Pre-Processing of Time Series 1.4.1 Transformation of variables 1.4.2 Differencing 1.4.3 Month-to-month basisand year-over-year 1.4.4 Moving average 1.5 Organization of This Book 1 1 6 9 9 10 11 12 14 17 2 The Covariance Function 2.1 The Distribution of Time Series and Stationarity 2.2 The Autocovariance Function of Stationary Time Series 2.3 Estimation of the Autocovariance and Autocorrelation Functions 2.4 Multivariate Time Series and Scatterplots 2.5 Cross-Covariance Function and Cross-Correlation Function 19 19 22 The Power Spectrum and the Periodogram 3.1 The Power Spectrum 3.2 The Periodogram 3.3 Averaging and Smoothing of the Periodogram 35 35 40 44 3 23 26 29
vi CONTENTS 3.4 3.5 Computational Method of Periodogram Computation of the Periodogram by Fast Fourier Transform 48 Statistical Modeling 4.1 Probability Distributions and Statistical Models 4.2 К-L Information and Entropy Maximization Principle 4.3 Estimation of the К-L Information and the Log-Likelihood 4.4 Estimation of Parameters by the Maximum Likelihood Method 4.5 AIC (Akaiké Information Criterion) 4.5.1 Eva!uation of C\ 4.5.2 Evaluation of C3 4.5.3 Evaluation of C2 4.5.4 Evaluationof C and AIC 4.6 Transformation of Data 55 55 60 The Least Squares Method 5.1 Regression Models and the Least Squares Method 5.2 The Least Squares Method Based on the Householder Transformation 5.3 Selection of Order by AIC 5.4 Addition of Data and Successive Householder Reduction 5.5 Variable Selection by AIC 79 79 6 Analysis of Time Series Using ARMA Models 6.1 ARMA Model 6.2 The Impulse Response Function 6.3 The Autocovariance Function 6.4 The Relation Between AR Coefficientsand PARCOR 6.5 The Power Spectrum of the ARMAProcess 6.6 The Characteristic Equation 6.7 The Multivariate AR Model 91 91 92 94 96 96 100 104 7 Estimation of an AR Model 7.1 Fitting an AR Model 7.2 Yule-Walker Methodand Levinson’s Algorithm 7.3 Estimation of an AR Model by the Least Squares Method 113 113 115 4 5 49 64 65 69 71 72 72 73 73 81 83 87 88 116
CONTHNTS 7.4 7.5 7.6 Hstimation of an AR Model by the PARCt )RMethod Large Sample Distribution of the Estimates Hstimation of Multivariate AR Model by the Yule-Walker Method Hstimation of Multivariate AR Model by the Least Squares Method 11H 121 The Locally Stationary AR Model 8.1 Locally Stationary AR Model 8.2 Automatic Partitioning of the Time Interval into an Arbitrary Number of Subintervals 8.3 Precise Hstimation of the Change Point 8.4 Posterior Probability of the Change Point 137 137 Analysis of Time Series with a State-Space Model 9.1 The State-Space Model 9.2 State Hstimation via the Kalman Hilter 9.3 Smoothing Algorithms 9.4 Long-Term Prediction of the Stale 9.5 Prediction of Time Series 9.6 Likelihood Computation and Parameter Hstimation for Time Series Models 9.7 Interpolation of Missing Observations 153 153 156 158 158 159 7.7 8 9 Vįį 124 ] 2у 139 144 149 163 166 10 Estimation of the ARMA Model 10.1 State-Space Representation of the ARMA Model 10.2 Initial State Distribution for an AR Model 10.3 Initial State Distribution of an ARMA Model 10.4 Maximum Likelihood Hstimates of an ARMAModel 10.5 Initial Hstimates of Parameters 171 171 172 174 175 178 11 Estimation of Trends 11.1 The Polynomial Trend Model 11.2 Trend Component Model - Model for GradualChanges 11.3 Trend Model 181 181 184 188 12 The Seasonal Adjustment Model 12.1 Seasonal Component Model 12.2 Standard Seasonal Adjustment Model 12.3 Decomposition Including a Stationary AR Component 12.4 Decomposition Including a Trading-Day Effect 195 195 198 201 206
viii CONTENTS 13 Time-Varying Coefficient AR Model 13.1 13.2 13.3 13.4 Time-Varying Variance Model Time-Varying Coefficient AR Model Estimation of the Time-Varying Spectrum The Assumption on System Noise for the Time-Varying Coefficient AR Model 13.5 Abrupt Changes of Coefficients 14 Non-Gaussian State-Space Model 14.1 14.2 14.3 14.4 14.5 Necessity of Non-Gaussian Models Non-Gaussian State-Space Models and State Estimation Numerical Computation of the State Estimation Fonnula Non-Gaussian Trend Model Non-symmetric Distribution ֊ A Time-Varying Variance Model 14.6 Applications of the Non-Gaussian State-Space Model 14.6.1 Processing of the outliers by a mixture of Gaussian distributions 14.6.2 A nonstationary discrete process 14.6.3 A direct method of estimating the time-varying variance 14.6.4 Nonlinear state-space models 15 Particle Filter 15.1 The Nonlinear Non-Gaussian State-Space Model and Approximations of Distributions 15.2 Particle Filter 15.2.1 One-step-ahead prediction 15.2.2 Filtering 15.2.3 Algorithm for the particle filter 15.2.4 Likelihood of a model 15.2.5 On the re-sampling method 15.2.6 Numerical examples 15.3 Particle Smoothing Method 15.4 Nonlinear Smoothing 16 Simulation 16.1 Generation of Uniform Random Numbers 16.2 Generation of White Noise 16.2.1 χ1 distribution 16.2.2 Cauchy distribution 16.2.3 Arbitrary distribution 213 213 217 222 224 225 229 229 230 232 235 240 244 245 245 246 247 249 249 263 253 253 254 254 255 256 259 262 267 267 269 272 272 272
CONTENTS 16.3 Simulation of ARMA models 16.4 Simulation Using a State-Space Model 16.5 Simulation with the Non-Gaussian State-Space Model ix 273 275 279 A Algorithms for Nonlinear Optimization 283 В Derivation of Levinson’s Algorithm 285 C Derivation of the Kalman Filter and Smoother Algorithms C.l Kalman Filter C.2 Smoothing 289 289 290 D Algorithm for the Particle Filter D.l One-Step-Ahead Prediction D.2 Filter D.3 Smoothing 293 293 294 295 Bibliography 311 Index 319 |
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| spelling | Kitagawa, Genshiro 1948- Verfasser (DE-588)1037417348 aut Introduction to time series modeling with applications in R Genshiro Kitagawa Second edition Boca Raton ; London ; New York CRC Press 2021 xvi, 323 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Monographs on Statistics and Applied Probability 166 Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 s R Programm (DE-588)4705956-4 s b DE-604 Erscheint auch als Online-Ausgabe 978-0-429-19796-3 Monographs on Statistics and Applied Probability 166 (DE-604)BV002494005 166 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032159884&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kitagawa, Genshiro 1948- Introduction to time series modeling with applications in R Monographs on Statistics and Applied Probability Zeitreihenanalyse (DE-588)4067486-1 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4067486-1 (DE-588)4705956-4 |
| title | Introduction to time series modeling with applications in R |
| title_auth | Introduction to time series modeling with applications in R |
| title_exact_search | Introduction to time series modeling with applications in R |
| title_exact_search_txtP | Introduction to time series modeling with applications in R |
| title_full | Introduction to time series modeling with applications in R Genshiro Kitagawa |
| title_fullStr | Introduction to time series modeling with applications in R Genshiro Kitagawa |
| title_full_unstemmed | Introduction to time series modeling with applications in R Genshiro Kitagawa |
| title_short | Introduction to time series modeling with applications in R |
| title_sort | introduction to time series modeling with applications in r |
| topic | Zeitreihenanalyse (DE-588)4067486-1 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Zeitreihenanalyse R Programm |
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