Modelling Financial Time Series with S-PLUS [推广有奖]

Customer ReviewsAvg. Customer Review: 
2 of 2 people found the following review helpful:

 This is the best applied financial econometrics book., October 28, 2002
 Reviewer: yin_luo (see more about me) from Toronto, Ontario Canada
This is an excellent book on financial econometrics, very practical yet rigorous. I wish all econometrics/statistics textbook could like this. Basic theory followed by practical examples - real life examples, not simplified ones like in other books. The authors gave detailed instructions on how to implement various econometric models, i.e. multi-factor models, GARCH, MGARCH, long memory models, state-space, etc. Most econometrics textbooks are at two extremes, they are either too theoretical (you still don't know how to put those models in real life), or too simple (lack of mathematical rigor and without advanced applications). This book is a combination of both worlds, computer codes/math models, and real life examples (some really good ones). A lot of cutting-edge techniques and advanced topics are also covered.

1 S and S-PLUS 3
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 S Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Assignment . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Class . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Modeling Functions in S+FinMetrics . . . . . . . . . . . . 10
1.3.1 Formula Specification . . . . . . . . . . . . . . . . . 10
1.3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.4 S-PLUS Resources . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Time Series Specification, Manipulation and Visualization
in S-PLUS 15
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 The Specification of “timeSeries” Objects in S-PLUS . . . 15
2.2.1 BasicManipulations . . . . . . . . . . . . . . . . . . 18
2.2.2 S-PLUS “timeDate” Objects . . . . . . . . . . . . . . 19
2.2.3 Creating Common “timeDate” Sequences . . . . . . 24
2.2.4 Miscellaneous Time and Date Functions . . . . . . . 28
2.2.5 Creating “timeSeries” Objects . . . . . . . . . . . 29
2.2.6 Aggregating and Disaggregating Time Series . . . . 30
2.2.7 Merging Time Series . . . . . . . . . . . . . . . . . . 38
iv Contents
2.2.8 Dealing withMissing Values Using the S+FinMetrics
Function interpNA . . . . . . . . . . . . . . . . . . . 39
2.3 Time Series Manipulation in S-PLUS . . . . . . . . . . . . . 40
2.3.1 Creating Lags and Differences . . . . . . . . . . . . . 40
2.3.2 Return Definitions . . . . . . . . . . . . . . . . . . . 43
2.3.3 Computing Asset Returns Using the S+FinMetrics
Function getReturns . . . . . . . . . . . . . . . . . 46
2.4 Visualizing Time Series in S-PLUS . . . . . . . . . . . . . . 48
2.4.1 Plotting “timeSeries” Using the S-PLUS Generic
plot Function . . . . . . . . . . . . . . . . . . . . . 48
2.4.2 Plotting “timeSeries” Using the S+FinMetrics Trellis
Plotting Functions . . . . . . . . . . . . . . . . . 51
References 55
3 Time Series Concepts 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Univariate Time Series . . . . . . . . . . . . . . . . . . . . . 58
3.2.1 Stationary and Ergodic Time Series . . . . . . . . . 58
3.2.2 Linear Processes and ARMAModels . . . . . . . . . 64
3.2.3 AutoregressiveModels . . . . . . . . . . . . . . . . . 66
3.2.4 Moving AverageModels . . . . . . . . . . . . . . . . 70
3.2.5 ARMA(p,q)Models . . . . . . . . . . . . . . . . . . 74
3.2.6 Estimation of ARMAModels and Forecasting . . . . 76
3.2.7 Martingales and Martingale Difference Sequences . . 83
3.2.8 Long-run Variance . . . . . . . . . . . . . . . . . . . 85
3.3 Univariate Nonstationary Time Series . . . . . . . . . . . . 88
3.4 LongMemory Time Series . . . . . . . . . . . . . . . . . . . 92
3.5 Multivariate Time Series . . . . . . . . . . . . . . . . . . . . 95
3.5.1 Stationary and Ergodic Multivariate Time Series . . 95
3.5.2 MultivariateWold Representation . . . . . . . . . . 100
3.5.3 Long Run Variance . . . . . . . . . . . . . . . . . . . 101
References 105
4 Unit Root Tests 107
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2 Testing for Nonstationarity and Stationarity . . . . . . . . . 108
4.3 Autoregressive Unit Root Tests . . . . . . . . . . . . . . . . 109
4.3.1 Simulating the DF and Normalized Bias Distributions 111
4.3.2 Trend Cases . . . . . . . . . . . . . . . . . . . . . . . 113
4.3.3 Dickey-Fuller Unit Root Tests . . . . . . . . . . . . . 116
4.3.4 Phillips-Perron Unit Root Tests . . . . . . . . . . . . 122
4.3.5 Some Problems with Unit Root Tests . . . . . . . . 124
4.4 Stationarity Tests . . . . . . . . . . . . . . . . . . . . . . . . 125
Contents v
4.4.1 Simulating the KPSS Distributions . . . . . . . . . . 126
4.4.2 Testing for Stationarity Using the S+FinMetrics Function
stationaryTest . . . . . . . . . . . . . . . . . 127
References 129
5 Modeling Extreme Values 131
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.2 ModelingMaxima andWorst Cases . . . . . . . . . . . . . . 132
5.2.1 The Fisher-Tippet Theorem and the Generalized Extreme
Value Distribution . . . . . . . . . . . . . . . 133
5.2.2 Estimation of the GEV Distribution . . . . . . . . . 137
5.2.3 Return Level . . . . . . . . . . . . . . . . . . . . . . 143
5.3 Modeling Extremes Over High Thresholds . . . . . . . . . . 146
5.3.1 The Limiting Distribution of Extremes Over High
Thresholds and the Generalized Pareto Distribution 148
5.3.2 Estimating the GPD byMaximumLikelihood . . . . 154
5.3.3 Estimating the Tails of the Loss Distribution . . . . 154
5.3.4 RiskMeasures . . . . . . . . . . . . . . . . . . . . . 158
5.4 Hill’s Non-parametric Estimator of Tail Index . . . . . . . . 162
5.4.1 Hill Tail and Quantile Estimation. . . . . . . . . . . 163
References 167
6 Time Series Regression Modeling 169
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2 Time Series RegressionModel . . . . . . . . . . . . . . . . . 170
6.2.1 Least Squares Estimation . . . . . . . . . . . . . . . 171
6.2.2 Goodness of Fit . . . . . . . . . . . . . . . . . . . . . 171
6.2.3 Hypothesis Testing . . . . . . . . . . . . . . . . . . . 172
6.2.4 Residual Diagnostics . . . . . . . . . . . . . . . . . . 173
6.3 Time Series Regression Using the S+FinMetrics Function OLS173
6.4 Dynamic Regression . . . . . . . . . . . . . . . . . . . . . . 188
6.4.1 Distributed Lags and Polynomial Distributed Lags . 192
6.4.2 Polynomial Distributed LagModels . . . . . . . . . 194
6.5 Heteroskedasticity and Autocorrelation Consistent CovarianceMatrix
Estimation . . . . . . . . . . . . . . . . . . . . 196
6.5.1 The Eicker-White Heteroskedasticity Consistent (HC)
CovarianceMatrix Estimate . . . . . . . . . . . . . . 196
6.5.2 Testing for Heteroskedasticity . . . . . . . . . . . . . 198
6.5.3 The Newey-West Heteroskedasticity and Autocorrelation
Consistent (HAC) Covariance Matrix Estimate 201
6.6 Recursive Least Squares Estimation . . . . . . . . . . . . . 205
6.6.1 CUSUM and CUSUMSQ Tests for Parameter Stability205
vi Contents
6.6.2 Computing Recursive Least Squares Estimates Using
the S+FinMetrics Function RLS . . . . . . . . . . . 206
References 211
7 Univariate GARCH Modeling 213
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
7.2 The Basic ARCHModel . . . . . . . . . . . . . . . . . . . . 214
7.2.1 Testing for ARCH Effects . . . . . . . . . . . . . . . 218
7.3 The GARCHModel and Its Properties . . . . . . . . . . . . 219
7.3.1 ARMA Representation of GARCHModel . . . . . . 220
7.3.2 GARCHModel and Stylized Facts . . . . . . . . . . 220
7.4 GARCH Modeling Using S+FinMetrics . . . . . . . . . . . 222
7.4.1 GARCHModel Estimation . . . . . . . . . . . . . . 222
7.4.2 GARCHModel Diagnostics . . . . . . . . . . . . . . 225
7.5 GARCHModel Extensions . . . . . . . . . . . . . . . . . . 230
7.5.1 Asymmetric Leverage Effects and News Impact . . . 231
7.5.2 Two ComponentsModel . . . . . . . . . . . . . . . . 237
7.5.3 GARCH-in-the-MeanModel . . . . . . . . . . . . . . 240
7.5.4 ARMA Terms and Exogenous Variables in ConditionalMean
Equation . . . . . . . . . . . . . . . . . 242
7.5.5 Exogenous Explanatory Variables in the Conditional
Variance Equation . . . . . . . . . . . . . . . . . . . 245
7.5.6 Non-Gaussian Error Distributions . . . . . . . . . . 246
7.6 GARCHModel Selection and Comparison . . . . . . . . . . 249
7.6.1 Constrained GARCH Estimation . . . . . . . . . . . 251
7.7 GARCHModel Prediction . . . . . . . . . . . . . . . . . . . 251
7.8 GARCHModel Simulation . . . . . . . . . . . . . . . . . . 254
7.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
References 259
8 Long Memory Time Series Modeling 263
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
8.2 LongMemory Time Series . . . . . . . . . . . . . . . . . . . 264
8.3 Statistical Tests for LongMemory . . . . . . . . . . . . . . 268
8.3.1 R/S Statistic . . . . . . . . . . . . . . . . . . . . . . 268
8.3.2 GPH Test . . . . . . . . . . . . . . . . . . . . . . . . 270
8.4 Estimation of LongMemory Parameter . . . . . . . . . . . 272
8.4.1 R/S Analysis . . . . . . . . . . . . . . . . . . . . . . 272
8.4.2 PeriodogramMethod . . . . . . . . . . . . . . . . . . 274
8.4.3 Whittle’sMethod . . . . . . . . . . . . . . . . . . . . 275
8.5 Estimation of FARIMA and SEMIFARModels . . . . . . . 276
8.5.1 Fractional ARIMAModels . . . . . . . . . . . . . . 277
8.5.2 SEMIFARModel . . . . . . . . . . . . . . . . . . . . 285
Contents vii
8.6 LongMemory GARCHModels . . . . . . . . . . . . . . . . 288
8.6.1 FIGARCH and FIEGARCHModels . . . . . . . . . 288
8.6.2 Estimation of LongMemory GARCHModels . . . . 290
8.6.3 Custom Estimation of Long Memory GARCH Models 293
8.7 Prediction fromLongMemoryModels . . . . . . . . . . . . 296
8.7.1 Prediction fromFARIMA/SEMIFARModels . . . . 297
8.7.2 Prediction from FIGARCH/FIEGARCH Models . . 300
References 303
9 Rolling Analysis of Time Series 307
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
9.2 Rolling Descriptive Statistics . . . . . . . . . . . . . . . . . 308
9.2.1 Univariate Statistics . . . . . . . . . . . . . . . . . . 308
9.2.2 Bivariate Statistics . . . . . . . . . . . . . . . . . . . 315
9.2.3 ExponentiallyWeightedMoving Averages . . . . . . 317
9.2.4 Moving Average Methods for Irregularly Spaced High
Frequency Data . . . . . . . . . . . . . . . . . . . . . 321
9.2.5 Rolling Analysis of Miscellaneous Functions . . . . . 328
9.3 Technical Analysis Indicators . . . . . . . . . . . . . . . . . 331
9.3.1 Price Indicators . . . . . . . . . . . . . . . . . . . . . 332
9.3.2 Momentum Indicators and Oscillators . . . . . . . . 332
9.3.3 Volatility Indicators . . . . . . . . . . . . . . . . . . 334
9.3.4 Volume Indicators . . . . . . . . . . . . . . . . . . . 335
9.4 Rolling Regression . . . . . . . . . . . . . . . . . . . . . . . 336
9.4.1 Estimating Rolling Regressions Using the S+FinMetrics
Function rollOLS . . . . . . . . . . . . . . . . . . . 337
9.4.2 Rolling Predictions and Backtesting . . . . . . . . . 343
9.5 Rolling Analysis of General Models Using the S+FinMetrics
Function roll . . . . . . . . . . . . . . . . . . . . . . . . . . 352
References 355
10 Systems of Regression Equations 357
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
10.2 Systems of Regression Equations . . . . . . . . . . . . . . . 358
10.3 Linear Seemingly Unrelated Regressions . . . . . . . . . . . 360
10.3.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . 360
10.3.2 Analysis of SUR Models with the S+FinMetrics Function
SUR . . . . . . . . . . . . . . . . . . . . . . . . . 363
10.4 Nonlinear Seemingly Unrelated RegressionModels . . . . . 370
10.4.1 Analysis of Nonlinear SUR Models with the S+FinMetrics
Function NLSUR . . . . . . . . . . . . . . . . . . . . . 371
References 379
viii Contents
11 Vector AutoregressiveModels forMultivariate Time Series381
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
11.2 The Stationary Vector AutoregressionModel . . . . . . . . 382
11.2.1 Estimation . . . . . . . . . . . . . . . . . . . . . . . 384
11.2.2 Inference on Coefficients . . . . . . . . . . . . . . . . 386
11.2.3 Lag Length Selection . . . . . . . . . . . . . . . . . . 386
11.2.4 Estimating VAR Models Using the S+FinMetrics
Function VAR . . . . . . . . . . . . . . . . . . . . . . 386
11.3 Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . 394
11.3.1 Traditional Forecasting Algorithm . . . . . . . . . . 394
11.3.2 Simulation-Based Forecasting . . . . . . . . . . . . . 398
11.4 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . 402
11.4.1 Granger Causality . . . . . . . . . . . . . . . . . . . 403
11.4.2 Impulse Response Functions . . . . . . . . . . . . . . 405
11.4.3 Forecast Error Variance Decompositions . . . . . . . 409
11.5 An Extended Example . . . . . . . . . . . . . . . . . . . . . 413
11.6 Bayesian Vector Autoregression . . . . . . . . . . . . . . . . 420
11.6.1 An Example of a Bayesian VARModel . . . . . . . 420
11.6.2 Conditional Forecasts . . . . . . . . . . . . . . . . . 423
References 425
12 Cointegration 427
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
12.2 Spurious Regression and Cointegration . . . . . . . . . . . . 428
12.2.1 Spurious Regression . . . . . . . . . . . . . . . . . . 428
12.2.2 Cointegration . . . . . . . . . . . . . . . . . . . . . . 431
12.2.3 Cointegration and Common Trends . . . . . . . . . . 433
12.2.4 Simulating Cointegrated Systems . . . . . . . . . . . 433
12.2.5 Cointegration and Error CorrectionModels . . . . . 437
12.3 Residual-Based Tests for Cointegration . . . . . . . . . . . . 440
12.3.1 Testing for Cointegration when the Cointegrating Vector
is Pre-specified . . . . . . . . . . . . . . . . . . . 440
12.3.2 Testing for Cointegration when the Cointegrating Vector
is Estimated . . . . . . . . . . . . . . . . . . . . 443
12.4 Regression-Based Estimates of Cointegrating Vectors and
Error CorrectionModels . . . . . . . . . . . . . . . . . . . . 446
12.4.1 Least Square Estimator . . . . . . . . . . . . . . . . 446
12.4.2 Stock and Watson’s Efficient Lead/Lag Estimator . 447
12.4.3 Estimating Error Correction Models by Least Squares 450
12.5 VARModels and Cointegration . . . . . . . . . . . . . . . . 451
12.5.1 The Cointegrated VAR . . . . . . . . . . . . . . . . 452
12.5.2 Johansen’s Methodology for Modeling Cointegration 454
12.5.3 Specification of Deterministic Terms . . . . . . . . . 455
Contents ix
12.5.4 Likelihood Ratio Tests for the Number of Cointegrating
Vectors . . . . . . . . . . . . . . . . . . . . . . . 457
12.5.5 Testing for the Number of Cointegrating Vectors Using
the S+FinMetrics Function coint . . . . . . . . 459
12.5.6 Maximum Likelihood Estimation of the Cointegrated
VECM. . . . . . . . . . . . . . . . . . . . . . . . . . 460
12.5.7 Maximum Likelihood Estimation of the Cointegrated
VECM Using the S+FinMetrics Function VECM . . . 462
12.5.8 Forecasting fromthe VECM . . . . . . . . . . . . . 465
12.6 Appendix: Maximum Likelihood Estimation of a Cointegrated
VECM . . . . . . . . . . . . . . . . . . . . . . . . . . 467
References 471
13 Multivariate GARCH Modeling 473
13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
13.2 ExponentiallyWeighted Covariance Estimate . . . . . . . . 474
13.3 Diagonal VEC Model . . . . . . . . . . . . . . . . . . . . . . 478
13.4 Multivariate GARCHModeling in FinMetrics . . . . . . . . 479
13.4.1 Multivariate GARCHModel Estimation . . . . . . . 479
13.4.2 Multivariate GARCHModel Diagnostics . . . . . . . 481
13.5 Multivariate GARCHModel Extensions . . . . . . . . . . . 488
13.5.1 Matrix-Diagonal Models . . . . . . . . . . . . . . . . 488
13.5.2 BEKKModels . . . . . . . . . . . . . . . . . . . . . 489
13.5.3 Univariate GARCH-basedModels . . . . . . . . . . 492
13.5.4 ARMA Terms and Exogenous Variables . . . . . . . 496
13.5.5 Multivariate Conditional t-Distribution . . . . . . . 499
13.6 Multivariate GARCH Prediction . . . . . . . . . . . . . . . 501
13.7 CustomEstimation of GARCHModels . . . . . . . . . . . . 504
13.7.1 GARCHModel Objects . . . . . . . . . . . . . . . . 504
13.7.2 Revision of GARCHModel Estimation . . . . . . . . 506
13.8 Multivariate GARCHModel Simulation . . . . . . . . . . . 507
References 511
14 State Space Models 513
14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
14.2 State Space Representation . . . . . . . . . . . . . . . . . . 514
14.2.1 Initial Conditions . . . . . . . . . . . . . . . . . . . . 515
14.2.2 State Space Representation in S+FinMetrics/SsfPack515
14.2.3 Missing Values . . . . . . . . . . . . . . . . . . . . . 521
14.2.4 S+FinMetrics/SsfPack Functions for Specifying the
State Space Form for Some Common Time Series
Models . . . . . . . . . . . . . . . . . . . . . . . . . 522
14.2.5 Simulating Observations from the State Space Model 534
x Contents
14.3 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
14.3.1 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . 536
14.3.2 Kalman Smoother . . . . . . . . . . . . . . . . . . . 537
14.3.3 Smoothed State and Response Estimates . . . . . . 538
14.3.4 Smoothed Disturbance Estimates . . . . . . . . . . . 538
14.3.5 Forecasting . . . . . . . . . . . . . . . . . . . . . . . 538
14.3.6 S+FinMetrics/SsfPack Implementation of State Space
Modeling Algorithms . . . . . . . . . . . . . . . . . . 538
14.4 Estimation of State SpaceModels . . . . . . . . . . . . . . . 547
14.4.1 Prediction Error Decomposition of Log-Likelihood . 547
14.4.2 Fitting State Space Models Using the S+FinMetrics/SsfPack
Function SsfFit . . . . . . . . . . . . . . . . . . . . 548
14.5 Simulation Smoothing . . . . . . . . . . . . . . . . . . . . . 553
References 557
15 Factor Models for Asset Returns 559
15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
15.2 Factor Model Specification . . . . . . . . . . . . . . . . . . . 560
15.3 Macroeconomic FactorModels for Returns . . . . . . . . . . 561
15.3.1 Sharpe’s Single IndexModel . . . . . . . . . . . . . 562
15.3.2 The GeneralMultifactorModel . . . . . . . . . . . . 567
15.4 Fundamental Factor Model . . . . . . . . . . . . . . . . . . 570
15.4.1 BARRA-type Single FactorModel . . . . . . . . . . 571
15.4.2 BARRA-type Industry FactorModel . . . . . . . . . 572
15.5 Statistical FactorModels for Returns . . . . . . . . . . . . . 580
15.5.1 Factor Analysis . . . . . . . . . . . . . . . . . . . . . 580
15.5.2 Principal Components . . . . . . . . . . . . . . . . . 587
15.5.3 Asymptotic Principal Components . . . . . . . . . . 595
15.5.4 Determining the Number of Factors . . . . . . . . . 600
References 605
16 Term Structure of Interest Rates 607
16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 607
16.2 Discount, Spot and Forward Rates . . . . . . . . . . . . . . 608
16.2.1 Definitions and Rate Conversion . . . . . . . . . . . 608
16.2.2 Rate Conversion in S+FinMetrics . . . . . . . . . . 609
16.3 Quadratic and Cubic Spline Interpolation . . . . . . . . . . 610
16.4 Smoothing Spline Interpolation . . . . . . . . . . . . . . . . 614
16.5 Nelson-Siegel Function . . . . . . . . . . . . . . . . . . . . . 618
16.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
References 625
17 Robust Change Detection 627
Contents xi
17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 627
17.2 REGARIMAModels . . . . . . . . . . . . . . . . . . . . . . 628
17.3 Robust Fitting of REGARIMAModels . . . . . . . . . . . . 629
17.4 Prediction Using REGARIMAModels . . . . . . . . . . . . 634
17.5 Controlling Robust Fitting of REGARIMAModels . . . . . 635
17.5.1 Adding Seasonal Effects . . . . . . . . . . . . . . . . 635
17.5.2 Controlling Outlier Detection . . . . . . . . . . . . . 637
17.5.3 Iterating the Procedure . . . . . . . . . . . . . . . . 639
17.6 Algorithms of Filtered τ-Estimation . . . . . . . . . . . . . 641
17.6.1 ClassicalMaximumLikelihood Estimates . . . . . . 642
17.6.2 Filtered τ-Estimates . . . . . . . . . . . . . . . . . . 643
References 645
Index 647

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