Modeling Financial Time Series with S-PLUS® (eBook)

Eric Zivot is an associate professor and Gary Waterman Distinguished Scholar in the Economics Department, and adjunct associate professor of finance in the Business School at the University of Washington. He regularly teaches courses on econometric theory, financial econometrics and time series econometrics, and is the recipient of the Henry T. Buechel Award for Outstanding Teaching. He is an associate editor of Studies in Nonlinear Dynamics and Econometrics. He has published papers in the leading econometrics journals, including Econometrica, Econometric Theory, the Journal of Business and Economic Statistics, Journal of Econometrics, and the Review of Economics and Statistics. Jiahui Wang is an employee of Ronin Capital LLC. He received a Ph.D. in Economics from the University of Washington in 1997. He has published in leading econometrics journals such as Econometrica and Journal of Business and Economic Statistics, and is the Principal Investigator of National Science Foundation SBIR grants. In 2002 Dr. Wang was selected as one of the "2000 Outstanding Scholars of the 21st Century" by International Biographical Centre.

Preface 5
References 10
Contents 11
S and S- PLUS 23
1.1 Introduction 23
1.2 S Objects 24
1.3 Modeling Functions in S+ FinMetrics 30
1.4 S- PLUS Resources 34
1.5 References 35
Time Series Specification, Manipulation, and Visualization in S- PLUS 37
2.1 Introduction 37
2.2 The Specification of "timeSeries” Objects in S- PLUS 37
2.3 Time Series Manipulation in S- PLUS 62
2.4 Visualizing Time Series in S- PLUS 70
2.5 References 77
Time Series Concepts 78
3.1 Introduction 78
3.2 Univariate Time Series 79
3.3 Univariate Nonstationary Time Series 114
3.4 Long Memory Time Series 118
3.5 Multivariate Time Series 122
3.6 References 130
Unit Root Tests 132
4.1 Introduction 132
4.2 Testing for Nonstationarity and Stationarity 133
4.3 Autoregressive Unit Root Tests 135
4.4 Stationarity Tests 150
4.5 Some Problems with Unit Root Tests 153
4.6 Efficient Unit Root Tests 153
4.7 References 159
Modeling Extreme Values 161
5.1 Introduction 161
5.2 Modeling Maxima and Worst Cases 162
5.3 Modeling Extremes Over High Thresholds 177
5.4 Hill’s Non-parametric Estimator of Tail Index 194
5.5 References 198
Time Series Regression Modeling 200
6.1 Introduction 200
6.2 Time Series Regression Model 201
6.3 Time Series Regression Using the S+ FinMetrics Function OLS 204
6.4 Dynamic Regression 220
6.5 Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation 227
6.6 Recursive Least Squares Estimation 236
6.7 References 240
Univariate GARCH Modeling 242
7.1 Introduction 242
7.2 The Basic ARCH Model 243
7.3 The GARCH Model and Its Properties 248
7.4 GARCH Modeling Using S+ FinMetrics 251
7.5 GARCH Model Extensions 259
7.6 GARCH Model Selection and Comparison 279
7.7 GARCH Model Prediction 281
7.8 GARCH Model Simulation 284
7.9 Conclusion 286
7.10 References 286
Long Memory Time Series Modeling 289
8.1 Introduction 289
8.2 Long Memory Time Series 290
8.3 Statistical Tests for Long Memory 294
8.4 Estimation of Long Memory Parameter 298
8.5 Estimation of FARIMA and SEMIFAR Models 302
8.6 Long Memory GARCH Models 314
8.7 Prediction from Long Memory Models 322
8.8 References 327
Rolling Analysis of Time Series 330
9.1 Introduction 330
9.2 Rolling Descriptive Statistics 331
9.3 Technical Analysis Indicators 354
9.4 Rolling Regression 359
9.5 Rolling Analysis of General Models Using the S+ FinMetrics Function roll 375
9.6 References 377
Systems of Regression Equations 378
10.1 Introduction 378
10.2 Systems of Regression Equations 379
10.3 Linear Seemingly Unrelated Regressions 381
10.4 Nonlinear Seemingly Unrelated Regression Models 391
10.5 References 399
Vector Autoregressive Models for Multivariate Time Series 401
11.1 Introduction 401
11.2 The Stationary Vector Autoregression Model 402
11.3 Forecasting 414
11.4 Structural Analysis 422
11.5 An Extended Example 432
11.6 Bayesian Vector Autoregression 440
11.7 References 444
Cointegration 446
12.1 Introduction 446
12.2 Spurious Regression and Cointegration 447
12.3 Residual-Based Tests for Cointegration 459
12.4 Regression-Based Estimates of Cointegrating Vectors and Error Correction Models 465
12.5 VAR Models and Cointegration 470
12.6 Appendix: Maximum Likelihood Estimation of a Cointegrated VECM 491
12.7 References 493
Multivariate GARCH Modeling 496
13.1 Introduction 496
13.2 Exponentially Weighted Covariance Estimate 497
13.3 Diagonal VEC Model 501
13.4 Multivariate GARCH Modeling in S+ FinMetrics 502
13.5 Multivariate GARCH Model Extensions 511
13.6 Multivariate GARCH Prediction 524
13.7 Custom Estimation of GARCH Models 527
13.8 Multivariate GARCH Model Simulation 530
13.9 References 532
State Space Models 534
14.1 Introduction 534
14.2 State Space Representation 535
14.3 Algorithms 558
14.4 Estimation of State Space Models 567
14.5 Simulation Smoothing 580
14.6 References 581
Factor Models for Asset Returns 583
15.1 Introduction 583
15.2 Factor Model Specification 584
15.3 Macroeconomic Factor Models for Returns 585
15.4 Fundamental Factor Model 594
15.5 Statistical Factor Models for Returns 604
15.6 References 628
Term Structure of Interest Rates 631
16.1 Introduction 631
16.2 Discount, Spot and Forward Rates 632
16.3 Quadratic and Cubic Spline Interpolation 634
16.4 Smoothing Spline Interpolation 638
16.5 Nelson-Siegel Function 642
16.6 Conclusion 646
16.7 References 647
Robust Change Detection 649
17.1 Introduction 649
17.2 REGARIMA Models 650
17.3 Robust Fitting of REGARIMA Models 651
17.4 Prediction Using REGARIMA Models 656
17.5 Controlling Robust Fitting of REGARIMA Models 657
17.6 Algorithms of Filtered Filtered -Estimation 663
17.7 References 665
Nonlinear Time Series Models 667
18.1 Introduction 667
18.2 BDS Test for Nonlinearity 668
18.3 Threshold Autoregressive Models 676
18.4 Smooth Transition Autoregressive Models 692
18.5 Markov Switching State Space Models 701
18.6 An Extended Example: Markov Switching Coincident Index 715
18.7 References 723
Copulas 727
19.1 Introduction 727
19.2 Motivating Example 728
19.3 Definitions and Basic Properties of Copulas 736
19.4 Parametric Copula Classes and Families 743
19.5 Fitting Copulas to Data 761
19.6 Risk Management Using Copulas 768
19.7 References 771
Continuous-Time Models for Financial Time Series 773
20.1 Introduction 773
20.2 SDEs: Background 774
20.3 Approximating Solutions to SDEs 775
20.4 S+ FinMetrics Functions for Solving SDEs 779
20.5 References 796
Generalized Method of Moments 798
21.1 Introduction 798
21.2 Single Equation Linear GMM 799
21.3 Estimation of S 806
21.4 GMM Estimation Using the S+ FinMetrics Function GMM 810
21.5 Hypothesis Testing for Linear Models 821
21.6 Nonlinear GMM 829
21.7 Examples of Nonlinear Models 832
21.8 References 855
Seminonparametric Conditional Density Models 859
22.1 Introduction 859
22.2 Overview of SNP Methodology 860
22.3 Estimating SNP Models in S+ FinMetrics 863
22.4 SNP Model Selection 892
22.5 SNP Model Diagnostics 903
22.6 Prediction from an SNP Model 909
22.7 Data Transformations 911
22.8 Examples 916
22.9 References 932
Efficient Method of Moments 935
23.1 Introduction 935
23.2 An Overview of the EMM Methodology 937
23.3 EMM Estimation in S+ FinMetrics 950
23.4 Examples 955
23.5 References 998
Index 1003