Regression models for time series analysis / Benjamin Kedem, Konstantinos Fokianos.

Format:

Book

Author/Creator:

Kedem, Benjamin, 1944-

Contributor:

Fokianos, Konstantinos.

Anne and Joseph Trachtman Memorial Book Fund.

Series:

Wiley series in probability and statistics

Language:

English

Subjects (All):

Time-series analysis.

Regression analysis.

Physical Description:

xiv, 337 pages : illustrations ; 25 cm.

Place of Publication:

Hoboken, NJ : John Wiley & Sons, Inc., [2002]

Contents:

1 Time Series Following Generalized Linear Models 1

1.1 Partial Likelihood 2

1.2 Generalized Linear Models and Time Series 4

1.3 Partial Likelihood Inference 10

1.3.1 Estimation of the Dispersion Parameter 14

1.3.2 Iterative Reweighted Least Squares 14

1.4 Asymptotic Theory 16

1.4.1 Uniqueness and Existence 17

1.4.2 Large Sample Properties 17

1.5 Testing Hypotheses 20

1.6 Diagnostics 23

1.6.1 Deviance 24

1.6.2 Model Selection Criteria 25

1.6.3 Residuals 25

1.7 Quasi-Partial Likelihood 28

1.7.1 Generalized Estimating Equations 31

1.8 Real Data Examples 33

1.8.1 A Note on Computation 33

1.8.2 A Note on Model Building 33

1.8.3 Analysis of Mortality Count Data 34

1.8.4 Application to Evapotranspiration 39

1.9 Problems and Complements 42

2 Regression Models for Binary Time Series 49

2.1 Link Functions for Binary Time Series 50

2.1.1 The Logistic Regression Model 51

2.1.2 Probit and Other Links 54

2.2 Partial Likelihood Estimation 56

2.3 Inference for Logistic Regression 59

2.3.1 Asymptotic Relative Efficiency 64

2.4 Goodness of Fit 65

2.4.1 Deviance 66

2.4.2 Goodness of Fit Based on Response Classification 66

2.5.1 Rainfall Prediction 70

2.5.2 Modeling Successive Eruptions 72

2.5.3 Stock Price Prediction 76

2.5.4 Modeling Sleep Data 79

2.6 Problems and Complements 81

3 Regression Models for Categorical Time Series 89

3.1 Modeling 90

3.2 Link Functions for Categorical Time Series 92

3.2.1 Models for Nominal Time Series 93

3.2.2 Models for Ordinal Time Series 97

3.3 Partial Likelihood Estimation 101

3.3.1 Inference for m=3 101

3.3.2 Inference for m>3 104

3.3.3 Large Sample Theory 107

3.3.4 Inference for the Multinomial Logit Model 108

3.3.5 Testing Hypotheses 109

3.4 Goodness of Fit 110

3.4.1 Goodness of Fit Based on Response Classification 111

3.4.2 Power Divergence Family of Goodness of Fit Tests 112

3.4.3 A Family of Goodness of Fit Tests 113

3.4.4 Further Diagnostic Tools 115

3.5.1 Explanatory Analysis of DNA Sequence Data 116

3.5.2 Soccer Forecasting 119

3.5.3 Sleep Data Revisited 121

3.6.1 Alternative Modeling 125

3.6.2 Spectral Analysis 125

3.6.3 Longitudinal Data 125

3.7 Problems and Complements 126

Appendix Asymptotic Theory 130

4 Regression Models for Count Time Series 139

4.1 Modeling 140

4.2 Models for Time Series of Counts 142

4.2.1 The Poisson Model 142

4.2.2 The Doubly Truncated Poisson Model 148

4.2.3 The Zeger

Qaqish Model 153

4.3 Inference 154

4.3.1 Partial Likelihood Estimation for the Poisson Model 154

4.3.2 Asymptotic Theory 156

4.3.3 Prediction Intervals 157

4.3.4 Inference for the Zeger

Qaqish Model 157

4.3.5 Hypothesis Testing 158

4.4 Goodness of Fit 159

4.4.1 Deviance 159

4.4.2 Residuals 159

4.5.1 Monthly Count of Rainy Days 160

4.5.2 Tourist Arrival Data 163

4.6 Problems and Complements 168

5 Other Models and Alternative Approaches 175

5.1 Integer Autoregressive and Moving Average Models 175

5.1.1 Branching Processes with Immigration 175

5.1.2 Integer Autoregressive Models of Order 1 178

5.1.3 Estimation for INAR(1) Process 183

5.1.4 Integer Autoregressive Models of Order p 184

5.1.5 Regression Analysis of Integer Autoregressive Models 185

5.1.6 Integer Moving Average Models 185

5.1.7 Extensions and Modifications 188

5.2 Discrete Autoregressive Moving Average Models 189

5.3 The Mixture Transition Distribution Model 190

5.3.1 Estimation in MTD Models 192

5.3.2 Old Faithful Data Revisited 192

5.3.3 Explanatory Analysis of DNA Sequence Data Revisited 193

5.3.4 Soccer Forecasting Data Revisited 193

5.4 Hidden Markov Models 194

5.5 Variable Mixture Models 197

5.5.1 Threshold Models 198

5.5.2 Partial Likelihood Inference 198

5.5.3 Comparison with the Threshold Model 199

5.6 ARCH Models 199

5.6.1 The ARCH(1) Model 199

5.6.2 Maximum Likelihood Estimation 200

5.6.3 Extensions of ARCH Models 200

5.7 Sinusoidal Regression Model 201

5.8 Mixed Models for Longitudinal Data 205

5.9 Problems and Complements 208

6 State Space Models 213

6.1.1 Historical Note 214

6.2 Linear Gaussian State Space Models 215

6.2.1 Examples of Linear State Space Models 216

6.2.2 Estimation by Kalman Filtering and Smoothing 218

6.2.3 Estimation in the Linear Gaussian Model 221

6.3 Nonlinear and Non-Gaussian State Space Models 223

6.3.1 General Filtering and Smoothing 225

6.3.2 Dynamic Generalized Linear Models 227

6.4 Simulation Based Methods for State Space Models 231

6.4.1 A Brief MCMC Tutorial 232

6.4.2 MCMC Inference for State Space Models 233

6.4.3 Sequential Monte Carlo Sampling Methods 237

6.4.4 Likelihood Inference 240

6.4.5 Longitudinal Data 241

6.5 Kalman Filtering in Space-Time Data 241

6.6 Problems and Complements 241

7 Prediction and Interpolation 249

7.1.1 Elements of Stationary Random Fields 251

7.1.2 Ordinary Kriging 252

7.2 Bayesian Spatial Prediction 258

7.2.1 An Auxiliary Gaussian Process 258

7.2.2 The Likelihood 260

7.2.3 Prior and Posterior of Model Parameters 262

7.2.4 Prediction of Z[subscript 0] 263

7.2.5 Numerical Algorithm for the Case k = 1 264

7.2.6 Normalizing Transformations 265

7.2.7 Software for BTG Implementation 265

7.3 Applications of BTG 267

7.3.1 Spatial Rainfall Prediction 267

7.3.2 Comparison with Kriging 274

7.3.3 Time Series Prediction 274

7.3.4 Seasonal Time Series 278

7.4 Problems and Complements 282

Appendix Elements of Stationary Processes 285.

Notes:

Includes biblographical references (pages 297-326) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

0471363553

OCLC:

50269705