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Title:
Modeling financial time series with S-plus
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Edition:
2nd ed.
Publication Information:
New York : Springer Verlag, 2006
ISBN:
9780387279657
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30000010102758 HG106 Z58 2006 Open Access Book Book
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Summary

Summary

This book represents an integration of theory, methods, and examples using the S-PLUS statistical modeling language and the S+FinMetrics module to facilitate the practice of financial econometrics. It is the first book to show the power of S-PLUS for the analysis of time series data. It is written for researchers and practitioners in the finance industry, academic researchers in economics and finance, and advanced MBA and graduate students in economics and finance.

Readers are assumed to have a basic knowledge of S-PLUS and a solid grounding in basic statistics and time series concepts. This edition covers S+FinMetrics 2.0 and includes new chapters.


Author Notes

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
Jiahui Wang is a Principal and Trading Research Officer at Barclays Global Investors


Table of Contents

Prefacep. v
1 S and S-PLUSp. 1
1.1 Introductionp. 1
1.2 S Objectsp. 2
1.2.1 Assignmentp. 2
1.2.2 Classp. 3
1.2.3 Methodp. 7
1.3 Modeling Functions in S+FinMetricsp. 8
1.3.1 Formula Specificationp. 8
1.3.2 Methodp. 11
1.4 S-PLUS Resourcesp. 12
1.4.1 Booksp. 12
1.4.2 Internetp. 13
1.5 Referencesp. 13
2 Time Series Specification, Manipulation, and Visualization in S-PLUSp. 15
2.1 Introductionp. 15
2.2 The Specification of "timeSeries" Objects in S-PLUSp. 15
2.2.1 Basic Manipulationsp. 18
2.2.2 S-PLUS "timeDate" Objectsp. 19
2.2.3 Creating Common "timeDate" Sequencesp. 24
2.2.4 Miscellaneous Time and Date Functionsp. 28
2.2.5 Creating "timeSeries" Objectsp. 28
2.2.6 Aggregating and Disaggregating Time Seriesp. 31
2.2.7 Merging Time Seriesp. 38
2.2.8 Dealing with Missing Values Using the S+FinMetrics Function interpNAp. 39
2.3 Time Series Manipulation in S-PLUSp. 40
2.3.1 Creating Lags and Differencesp. 40
2.3.2 Return Definitionsp. 43
2.3.3 Computing Asset Returns Using the S+FinMetrics Function getReturnsp. 46
2.4 Visualizing Time Series in S-PLUSp. 48
2.4.1 Plotting "timeSeries" Using the S-PLUS Generic plot Functionp. 48
2.4.2 Plotting "timeSeries" Using the S+FinMetrics Trellis Plotting Functionsp. 52
2.5 Referencesp. 55
3 Time Series Conceptsp. 57
3.1 Introductionp. 57
3.2 Univariate Time Seriesp. 58
3.2.1 Stationary and Ergodic Time Seriesp. 58
3.2.2 Linear Processes and ARMA Modelsp. 64
3.2.3 Autoregressive Modelsp. 66
3.2.4 Moving Average Modelsp. 71
3.2.5 ARMA(p,q) Modelsp. 74
3.2.6 Estimation of ARMA Models and Forecastingp. 76
3.2.7 Martingales and Martingale Difference Sequencesp. 83
3.2.8 Long-run Variancep. 85
3.2.9 Variance Ratiosp. 88
3.3 Univariate Nonstationary Time Seriesp. 93
3.4 Long Memory Time Seriesp. 97
3.5 Multivariate Time Seriesp. 101
3.5.1 Stationary and Ergodic Multivariate Time Seriesp. 101
3.5.2 Multivariate Wold Representationp. 106
3.5.3 Long Run Variancep. 107
3.6 Referencesp. 109
4 Unit Root Testsp. 111
4.1 Introductionp. 111
4.2 Testing for Nonstationarity and Stationarityp. 112
4.3 Autoregressive Unit Root Testsp. 114
4.3.1 Simulating the DF and Normalized Bias Distributionsp. 116
4.3.2 Trend Casesp. 118
4.3.3 Dickey-Fuller Unit Root Testsp. 120
4.3.4 Phillips-Perron Unit Root Testsp. 127
4.4 Stationarity Testsp. 129
4.4.1 Simulating the KPSS Distributionsp. 130
4.4.2 Testing for Stationarity Using the S+FinMetrics Function stationaryTestp. 131
4.5 Some Problems with Unit Root Testsp. 132
4.6 Efficient Unit Root Testsp. 132
4.6.1 Point Optimal Testsp. 133
4.6.2 DF-GLS Testsp. 134
4.6.3 Modified Efficient PP Testsp. 134
4.6.4 Estimating [lambda superscript 2]p. 135
4.6.5 Choosing Lag Lengths to Achieve Good Size and Powerp. 135
4.7 Referencesp. 138
5 Modeling Extreme Valuesp. 141
5.1 Introductionp. 141
5.2 Modeling Maxima and Worst Casesp. 142
5.2.1 The Fisher-Tippet Theorem and the Generalized Extreme Value Distributionp. 143
5.2.2 Estimation of the GEV Distributionp. 147
5.2.3 Return Levelp. 153
5.3 Modeling Extremes Over High Thresholdsp. 157
5.3.1 The Limiting Distribution of Extremes Over High Thresholds and the Generalized Pareto Distributionp. 159
5.3.2 Estimating the GPD by Maximum Likelihoodp. 164
5.3.3 Estimating the Tails of the Loss Distributionp. 165
5.3.4 Risk Measuresp. 171
5.4 Hill's Non-parametric Estimator of Tail Indexp. 174
5.4.1 Hill Tail and Quantile Estimationp. 175
5.5 Referencesp. 178
6 Time Series Regression Modelingp. 181
6.1 Introductionp. 181
6.2 Time Series Regression Modelp. 182
6.2.1 Least Squares Estimationp. 183
6.2.2 Goodness of Fitp. 183
6.2.3 Hypothesis Testingp. 184
6.2.4 Residual Diagnosticsp. 185
6.3 Time Series Regression Using the S+FinMetrics Function OLSp. 185
6.4 Dynamic Regressionp. 201
6.4.1 Distributed Lags and Polynomial Distributed Lagsp. 205
6.4.2 Polynomial Distributed Lag Modelsp. 207
6.5 Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimationp. 208
6.5.1 The Eicker-White Heteroskedasticity Consistent (HC) Covariance Matrix Estimatep. 209
6.5.2 Testing for Heteroskedasticityp. 211
6.5.3 The Newey-West Heteroskedasticity and Autocorrelation Consistent (HAC) Covariance Matrix Estimatep. 214
6.6 Recursive Least Squares Estimationp. 217
6.6.1 CUSUM and CUSUMSQ Tests for Parameter Stabilityp. 218
6.6.2 Computing Recursive Least Squares Estimates Using the S+FinMetrics Function RLSp. 219
6.7 Referencesp. 221
7 Univariate GARCH Modelingp. 223
7.1 Introductionp. 223
7.2 The Basic ARCH Modelp. 224
7.2.1 Testing for ARCH Effectsp. 228
7.3 The GARCH Model and Its Propertiesp. 229
7.3.1 ARMA Representation of GARCH Modelp. 230
7.3.2 GARCH Model and Stylized Factsp. 230
7.4 GARCH Modeling Using S+FinMetricsp. 232
7.4.1 GARCH Model Estimationp. 232
7.4.2 GARCH Model Diagnosticsp. 235
7.5 GARCH Model Extensionsp. 240
7.5.1 Asymmetric Leverage Effects and News Impactp. 241
7.5.2 Two Components Modelp. 247
7.5.3 GARCH-in-the-Mean Modelp. 250
7.5.4 ARMA Terms and Exogenous Variables in Conditional Mean Equationp. 252
7.5.5 Exogenous Explanatory Variables in the Conditional Variance Equationp. 254
7.5.6 Non-Gaussian Error Distributionsp. 257
7.6 GARCH Model Selection and Comparisonp. 260
7.6.1 Constrained GARCH Estimationp. 261
7.7 GARCH Model Predictionp. 262
7.8 GARCH Model Simulationp. 265
7.9 Conclusionp. 267
7.10 Referencesp. 267
8 Long Memory Time Series Modelingp. 271
8.1 Introductionp. 271
8.2 Long Memory Time Seriesp. 272
8.3 Statistical Tests for Long Memoryp. 276
8.3.1 R/S Statisticp. 276
8.3.2 GPH Testp. 278
8.4 Estimation of Long Memory Parameterp. 280
8.4.1 R/S Analysisp. 280
8.4.2 Periodogram Methodp. 282
8.4.3 Whittle's Methodp. 283
8.5 Estimation of FARIMA and SEMIFAR Modelsp. 284
8.5.1 Fractional ARIMA Modelsp. 285
8.5.2 SEMIFAR Modelp. 292
8.6 Long Memory GARCH Modelsp. 296
8.6.1 FIGARCH and FIEGARCH Modelsp. 296
8.6.2 Estimation of Long Memory GARCH Modelsp. 297
8.6.3 Custom Estimation of Long Memory GARCH Modelsp. 301
8.7 Prediction from Long Memory Modelsp. 304
8.7.1 Prediction from FARIMA/SEMIFAR Modelsp. 304
8.7.2 Prediction from FIGARCH/FIEGARCH Modelsp. 308
8.8 Referencesp. 309
9 Rolling Analysis of Time Seriesp. 313
9.1 Introductionp. 313
9.2 Rolling Descriptive Statisticsp. 314
9.2.1 Univariate Statisticsp. 314
9.2.2 Bivariate Statisticsp. 321
9.2.3 Exponentially Weighted Moving Averagesp. 323
9.2.4 Moving Average Methods for Irregularly Spaced High Frequency Datap. 327
9.2.5 Rolling Analysis of Miscellaneous Functionsp. 334
9.3 Technical Analysis Indicatorsp. 337
9.3.1 Price Indicatorsp. 338
9.3.2 Momentum Indicators and Oscillatorsp. 338
9.3.3 Volatility Indicatorsp. 340
9.3.4 Volume Indicatorsp. 341
9.4 Rolling Regressionp. 342
9.4.1 Estimating Rolling Regressions Using the S+FinMetrics Function rollOLSp. 343
9.4.2 Rolling Predictions and Backtestingp. 349
9.5 Rolling Analysis of General Models Using the S+FinMetrics Function rollp. 358
9.6 Referencesp. 360
10 Systems of Regression Equationsp. 361
10.1 Introductionp. 361
10.2 Systems of Regression Equationsp. 362
10.3 Linear Seemingly Unrelated Regressionsp. 364
10.3.1 Estimationp. 364
10.3.2 Analysis of SUR Models with the S+FinMetrics Function SURp. 367
10.4 Nonlinear Seemingly Unrelated Regression Modelsp. 374
10.4.1 Analysis of Nonlinear SUR Models with the S+FinMetrics Function NLSURp. 375
10.5 Referencesp. 382
11 Vector Autoregressive Models for Multivariate Time Seriesp. 385
11.1 Introductionp. 385
11.2 The Stationary Vector Autoregression Modelp. 386
11.2.1 Estimationp. 388
11.2.2 Inference on Coefficientsp. 390
11.2.3 Lag Length Selectionp. 390
11.2.4 Estimating VAR Models Using the S+FinMetrics Function VARp. 390
11.3 Forecastingp. 398
11.3.1 Traditional Forecasting Algorithmp. 398
11.3.2 Simulation-Based Forecastingp. 402
11.4 Structural Analysisp. 406
11.4.1 Granger Causalityp. 407
11.4.2 Impulse Response Functionsp. 409
11.4.3 Forecast Error Variance Decompositionsp. 414
11.5 An Extended Examplep. 416
11.6 Bayesian Vector Autoregressionp. 424
11.6.1 An Example of a Bayesian VAR Modelp. 424
11.6.2 Conditional Forecastsp. 427
11.7 Referencesp. 428
12 Cointegrationp. 431
12.1 Introductionp. 431
12.2 Spurious Regression and Cointegrationp. 432
12.2.1 Spurious Regressionp. 432
12.2.2 Cointegrationp. 435
12.2.3 Cointegration and Common Trendsp. 437
12.2.4 Simulating Cointegrated Systemsp. 437
12.2.5 Cointegration and Error Correction Modelsp. 441
12.3 Residual-Based Tests for Cointegrationp. 444
12.3.1 Testing for Cointegration When the Cointegrating Vector Is Pre-specifiedp. 444
12.3.2 Testing for Cointegration When the Cointegrating Vector Is Estimatedp. 447
12.4 Regression-Based Estimates of Cointegrating Vectors and Error Correction Modelsp. 450
12.4.1 Least Square Estimatorp. 450
12.4.2 Stock and Watson's Efficient Lead/Lag Estimatorp. 451
12.4.3 Estimating Error Correction Models by Least Squaresp. 454
12.5 VAR Models and Cointegrationp. 455
12.5.1 The Cointegrated VARp. 456
12.5.2 Johansen's Methodology for Modeling Cointegrationp. 458
12.5.3 Specification of Deterministic Termsp. 459
12.5.4 Likelihood Ratio Tests for the Number of Cointegrating Vectorsp. 461
12.5.5 Testing Hypothesis on Cointegrating Vectors Using the S+FinMetrics Function cointp. 463
12.5.6 Maximum Likelihood Estimation of the Cointegrated VECMp. 467
12.5.7 Maximum Likelihood Estimation of the Cointegrated VECM Using the S+FinMetrics Function VECMp. 468
12.5.8 Forecasting from the VECMp. 474
12.6 Appendix: Maximum Likelihood Estimation of a Cointegrated VECMp. 476
12.7 Referencesp. 478
13 Multivariate GARCH Modelingp. 481
13.1 Introductionp. 481
13.2 Exponentially Weighted Covariance Estimatep. 482
13.3 Diagonal VEC Modelp. 486
13.4 Multivariate GARCH Modeling in S+FinMetricsp. 487
13.4.1 Multivariate GARCH Model Estimationp. 487
13.4.2 Multivariate GARCH Model Diagnosticsp. 490
13.5 Multivariate GARCH Model Extensionsp. 496
13.5.1 Matrix-Diagonal Modelsp. 496
13.5.2 BEKK Modelsp. 498
13.5.3 Univariate GARCH-based Modelsp. 499
13.5.4 ARMA Terms and Exogenous Variablesp. 504
13.5.5 Multivariate Conditional t-Distributionp. 508
13.6 Multivariate GARCH Predictionp. 509
13.7 Custom Estimation of GARCH Modelsp. 512
13.7.1 GARCH Model Objectsp. 512
13.7.2 Revision of GARCH Model Estimationp. 514
13.8 Multivariate GARCH Model Simulationp. 515
13.9 Referencesp. 517
14 State Space Modelsp. 519
14.1 Introductionp. 519
14.2 State Space Representationp. 520
14.2.1 Initial Conditionsp. 521
14.2.2 State Space Representation in S+FinMetrics/SsfPackp. 521
14.2.3 Missing Valuesp. 527
14.2.4 S+FinMetrics/SsfPack Functions for Specifying the State Space Form for Some Common Time Series Modelsp. 528
14.2.5 Simulating Observations from the State Space Modelp. 540
14.3 Algorithmsp. 543
14.3.1 Kalman Filterp. 543
14.3.2 Kalman Smootherp. 543
14.3.3 Smoothed State and Response Estimatesp. 544
14.3.4 Smoothed Disturbance Estimatesp. 544
14.3.5 Forecastingp. 544
14.3.6 S+FinMetrics/SsfPack Implementation of State Space Modeling Algorithmsp. 545
14.4 Estimation of State Space Modelsp. 552
14.4.1 Prediction Error Decomposition of Log-Likelihoodp. 552
14.4.2 Fitting State Space Models Using the S+FinMetrics/SsfPack Function SsfFitp. 554
14.4.3 Quasi-Maximum Likelihood Estimationp. 561
14.5 Simulation Smoothingp. 565
14.6 Referencesp. 566
15 Factor Models for Asset Returnsp. 569
15.1 Introductionp. 569
15.2 Factor Model Specificationp. 570
15.3 Macroeconomic Factor Models for Returnsp. 571
15.3.1 Sharpe's Single Index Modelp. 572
15.3.2 The General Multifactor Modelp. 577
15.4 Fundamental Factor Modelp. 580
15.4.1 BARRA-type Single Factor Modelp. 581
15.4.2 BARRA-type Industry Factor Modelp. 582
15.5 Statistical Factor Models for Returnsp. 590
15.5.1 Factor Analysisp. 590
15.5.2 Principal Componentsp. 597
15.5.3 Asymptotic Principal Componentsp. 606
15.5.4 Determining the Number of Factorsp. 610
15.6 Referencesp. 614
16 Term Structure of Interest Ratesp. 617
16.1 Introductionp. 617
16.2 Discount, Spot and Forward Ratesp. 618
16.2.1 Definitions and Rate Conversionp. 618
16.2.2 Rate Conversion in S+FinMetricsp. 619
16.3 Quadratic and Cubic Spline Interpolationp. 620
16.4 Smoothing Spline Interpolationp. 624
16.5 Nelson-Siegel Functionp. 628
16.6 Conclusionp. 632
16.7 Referencesp. 633
17 Robust Change Detectionp. 635
17.1 Introductionp. 635
17.2 REGARIMA Modelsp. 636
17.3 Robust Fitting of REGARIMA Modelsp. 637
17.4 Prediction Using REGARIMA Modelsp. 642
17.5 Controlling Robust Fitting of REGARIMA Modelsp. 643
17.5.1 Adding Seasonal Effectsp. 643
17.5.2 Controlling Outlier Detectionp. 645
17.5.3 Iterating the Procedurep. 647
17.6 Algorithms of Filtered [tau]-Estimationp. 649
17.6.1 Classical Maximum Likelihood Estimatesp. 650
17.6.2 Filtered [tau]-Estimatesp. 651
17.7 Referencesp. 651
18 Nonlinear Time Series Modelsp. 653
18.1 Introductionp. 653
18.2 BDS Test for Nonlinearityp. 654
18.2.1 BDS Test Statisticp. 655
18.2.2 Size of BDS Testp. 655
18.2.3 BDS Test as a Nonlinearity Test and a Misspecification Testp. 657
18.3 Threshold Autoregressive Modelsp. 662
18.3.1 TAR and SETAR Modelsp. 663
18.3.2 Tsay's Approachp. 664
18.3.3 Hansen's Approachp. 671
18.4 Smooth Transition Autoregressive Modelsp. 678
18.4.1 Logistic and Exponential STAR Modelsp. 678
18.4.2 Test for STAR Nonlinearityp. 680
18.4.3 Estimation of STAR Modelsp. 683
18.5 Markov Switching State Space Modelsp. 687
18.5.1 Discrete State Markov Processp. 688
18.5.2 Markov Switching AR Processp. 690
18.5.3 Markov Switching State Space Modelsp. 691
18.6 An Extended Example: Markov Switching Coincident Indexp. 701
18.6.1 State Space Representation of Markov Switching Coincident Index Modelp. 702
18.6.2 Approximate MLE of Markov Switching Coincident Indexp. 705
18.7 Referencesp. 709
19 Copulasp. 713
19.1 Introductionp. 713
19.2 Motivating Examplep. 714
19.3 Definitions and Basic Properties of Copulasp. 722
19.3.1 Properties of Distributionsp. 722
19.3.2 Copulas and Sklar's Theoremp. 724
19.3.3 Dependence Measures and Copulasp. 726
19.4 Parametric Copula Classes and Familiesp. 729
19.4.1 Normal Copulap. 729
19.4.2 Normal Mixture Copulap. 730
19.4.3 Extreme Value Copula Classp. 730
19.4.4 Archimedean Copulasp. 732
19.4.5 Archimax Copulasp. 735
19.4.6 Representation of Copulas in S+FinMetricsp. 735
19.4.7 Creating Arbitrary Bivariate Distributionsp. 743
19.4.8 Simulating from Arbitrary Bivariate Distributionsp. 745
19.5 Fitting Copulas to Datap. 747
19.5.1 Empirical Copulap. 747
19.5.2 Maximum Likelihood Estimationp. 750
19.5.3 Fitting Copulas Using the S+FinMetrics/EVANESCE Function fit.copulap. 751
19.6 Risk Management Using Copulasp. 754
19.6.1 Computing Portfolio Risk Measures Using Copulasp. 754
19.6.2 Computing VaR and ES by Simulationp. 755
19.7 Referencesp. 757
20 Continuous-Time Models for Financial Time Seriesp. 759
20.1 Introductionp. 759
20.2 SDEs: Backgroundp. 760
20.3 Approximating Solutions to SDEsp. 761
20.4 S+FinMetrics Functions for Solving SDEsp. 765
20.4.1 Problem-Specific Simulatorsp. 765
20.4.2 General Simulatorsp. 771
20.5 Referencesp. 782
21 Generalized Method of Momentsp. 785
21.1 Introductionp. 785
21.2 Single Equation Linear GMMp. 786
21.2.1 Definition of the GMM Estimatorp. 787
21.2.2 Specification Tests in Overidentified Modelsp. 791
21.2.3 Two-Stage Least Squares as an Efficient GMM Estimatorp. 792
21.3 Estimation of Sp. 793
21.3.1 Serially Uncorrelated Momentsp. 794
21.3.2 Serially Correlated Momentsp. 794
21.3.3 Estimating S Using the S+FinMetrics Function var.hacp. 797
21.4 GMM Estimation Using the S+FinMetrics Function GMMp. 797
21.5 Hypothesis Testing for Linear Modelsp. 808
21.5.1 Testing Restrictions on Coefficientsp. 808
21.5.2 Testing Subsets of Orthogonality Conditionsp. 812
21.5.3 Testing Instrument Relevancep. 813
21.6 Nonlinear GMMp. 816
21.6.1 Asymptotic Propertiesp. 818
21.6.2 Hypothesis Tests for Nonlinear Modelsp. 819
21.7 Examples of Nonlinear Modelsp. 819
21.7.1 Student's t Distributionp. 819
21.7.2 MA(1) Modelp. 821
21.7.3 Euler Equation Asset Pricing Modelp. 827
21.7.4 Stochastic Volatility Modelp. 833
21.7.5 Interest Rate Diffusion Modelp. 838
21.8 Referencesp. 842
22 Seminonparametric Conditional Density Modelsp. 847
22.1 Introductionp. 847
22.2 Overview of SNP Methodologyp. 848
22.3 Estimating SNP Models in S+FinMetricsp. 851
22.3.1 Example Datap. 853
22.3.2 Markovian Time Series and the Gaussian Vector Autoregression Modelp. 855
22.3.3 Hermite Expansion and the Semiparametric VARp. 860
22.3.4 Conditional Heterogeneityp. 868
22.3.5 ARCH/GARCH Leading Termp. 874
22.4 SNP Model Selectionp. 880
22.4.1 Random Restartsp. 881
22.4.2 The expand Functionp. 886
22.4.3 The SNP.auto Functionp. 889
22.5 SNP Model Diagnosticsp. 891
22.5.1 Residual Analysisp. 892
22.5.2 Simulationp. 896
22.6 Prediction from an SNP Modelp. 897
22.7 Data Transformationsp. 899
22.7.1 Centering and Scaling Transformationp. 899
22.7.2 Transformations to Deal with Heavy Tailed Datap. 901
22.7.3 Transformation to Deal with Small SNP Density Valuesp. 903
22.8 Examplesp. 904
22.8.1 SNP Models for Daily Returns on Microsoft Stockp. 904
22.8.2 SNP Models for Daily Returns on the S&P 500 Indexp. 909
22.8.3 SNP Models for Weekly 3-Month U.S. T-Bill Ratesp. 914
22.9 Referencesp. 920
23 Efficient Method of Momentsp. 923
23.1 Introductionp. 923
23.2 An Overview of the EMM Methodologyp. 925
23.2.1 Continuous-Time Stochastic Volatility Model for Interest Ratesp. 925
23.2.2 Minimum Chi-Squared Estimatorsp. 928
23.2.3 Efficiency Considerationsp. 930
23.2.4 A General Purpose Auxiliary Modelp. 935
23.2.5 The Projection Stepp. 935
23.2.6 The Estimation Stepp. 936
23.3 EMM Estimation in S+FinMetricsp. 938
23.3.1 Simulator Functionsp. 940
23.3.2 SNP Auxiliary Model Estimationp. 943
23.4 Examplesp. 943
23.4.1 MA(1) Modelp. 944
23.4.2 Discrete-Time Stochastic Volatility Modelsp. 954
23.4.3 Interest Rate Diffusion Modelsp. 966
23.5 Referencesp. 986
Indexp. 991
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