Statistical analysis of financial data in R:
Gespeichert in:
| Vorheriger Titel: | Carmona, René Statistical analysis of financial data in S-PLUS |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2014
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 588 S. graph. Darst. |
| ISBN: | 9781461487876 9781493938353 |
Internformat
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| 245 | 1 | 0 | |a Statistical analysis of financial data in R |c René A. Carmona |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2014 | |
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| 650 | 4 | |a Finances - Modèles économétriques | |
| 650 | 7 | |a Finanças (modelos matemáticos) |2 larpcal | |
| 650 | 7 | |a Matemática financeira |2 larpcal | |
| 650 | 7 | |a Portfolio-analyse |2 gtt | |
| 650 | 7 | |a S-Plus |2 gtt | |
| 650 | 7 | |a Statistische analyse |2 gtt | |
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Ökonometrisches Modell | |
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| 780 | 0 | 0 | |i 1. Auflage |a Carmona, René |t Statistical analysis of financial data in S-PLUS |
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| adam_text | Titel: Statistical analysis of financial data in R
Autor: Carmona, René
Jahr: 2014
Contents
Part I DATA EXPLORATION, ESTIMATION
AND SIMULATION 1
1 UNIVARIATE DATA DISTRIBUTIONS 3
1.1 Probability Distributions and Their Parameters....................................3
1.1.1 Standard Probability Distribution Families..............................3
1.1.2 Estimation from Empirical Data................................................18
1.1.3 Quantiles and Q-Q Plots............................................................22
1.2 Observations and Nonparametric Density Estimation..........................31
1.2.1 Sample Data................................................................................31
1.2.2 Nonparametric Estimation..........................................................35
1.2.3 Histograms..................................................................................39
1.2.4 Kernel Density Estimation..........................................................41
1.2.5 Empirical Q-Q Plots....................................................................48
1.3 Monte Carlo Computations....................................................................49
1.3.1 Generating Random Samples in R............................................49
1.3.2 Limit Theorems and Monte Carlo Computations....................51
1.3.3 Home Grown Random Samples................................................60
Problems............................................................................................................62
Notes Complements......................................................................................67
2 HEAVY TAIL DISTRIBUTIONS 69
2.1 A Primer on Extreme Value Theory......................................................69
2.1.1 Empirical Evidence of Extreme Events....................................69
2.1.2 Pareto Distributions....................................................................71
2.1.3 Tidbits of Extreme Value Theory..............................................75
2.2 GEV GPD Parameter Estimation ......................................................83
2.2.1 The Method of L-Moments........................................................83
2.2.2 Maximum Likelihood Estimation..............................................90
2.2.3 An Example Chosen for Pedagogical Reasons........................93
2.2.4 Implementation of the Block-Maxima Method........................95
2.3 Semi Parametric Estimation....................................................................97
2.3.1 Threshold Exceedances..............................................................97
2.3.2 Semi Parametric Estimation......................................................100
2.3.3 The Example of the PCS Index Revisited................................102
2.3.4 The Example of the Weekly S P Returns................................106
Appendix: Risk Measures: Why and What For?............................................109
Problems............................................................................................................114
Notes Complements......................................................................................118
3 DEPENDENCE MULTIVARIATE DATA EXPLORATION 121
3.1 Multivariate Data and First Measure of Dependence ..........................121
3.1.1 Density Estimation......................................................................123
3.1.2 The Correlation Coefficient........................................................126
3.2 The Multivariate Normal Distribution....................................................128
3.2.1 Important Remark about Independence....................................130
3.2.2 Simulation of Random Samples................................................130
3.2.3 The Bivariate Case......................................................................131
3.2.4 A Simulation Example................................................................132
3.2.5 Let s Have Some Coffee............................................................133
3.2.6 Is the Joint Distribution Normal?..............................................134
3.3 Marginals and More Measures of Dependence....................................135
3.3.1 Estimation of the Coffee Log-Return Distributions................136
3.3.2 More Measures of Dependence..................................................142
3.4 Copulas......................................................................................................144
3.4.1 Definitions and First Properties..................................................145
3.4.2 Examples of Copula Families....................................................146
3.4.3 Copulas and General Bivariate Distributions............................148
3.4.4 Fitting Copulas............................................................................151
3.4.5 Monte Carlo Simulations with Copulas....................................152
3.4.6 A Risk Management Example ..................................................154
3.4.7 A First Example from the Credit Markets................................157
3.4.8 Higher Dimensional Copulas ....................................................158
3.4.9 Multi Name Credit Derivatives and CDOs..............................164
3.5 Principal Component Analysis ..............................................................171
3.5.1 Identification of the Principal Components of a Data Set ... 172
3.5.2 PCA with R..................................................................................175
3.5.3 Effective Dimension of the Space of Yield Curves..................175
3.5.4 Swap Rate Curves ......................................................................178
Appendix 1 : Calculus with Random Vectors and Matrices..........................180
Appendix 2: Families of Copulas....................................................................183
Problems............................................................................................................186
Notes Complements......................................................................................195
Part II REGRESSION 197
4 PARAMETRIC REGRESSION 199
4.1 Simple Linear Regression.................................... 199
4.1.1 Getting the Data..................................... 200
4.1.2 First Plots .......................................... 201
4.1.3 Regression Set-up.................................... 202
4.1.4 Simple Linear Regression............................. 205
4.1.5 Cost Minimizations.................................. 208
4.1.6 Regression as a Minimization Problem.................. 209
4.2 Regression for Prediction Sensitivities....................... 211
4.2.1 Prediction.......................................... 211
4.2.2 Introductory Discussion of Sensitivity and Robustness..... 213
4.2.3 Comparing L2 and LI Regressions ..................... 214
4.2.4 Taking Another Look at the Coffee Data................. 216
4.3 Smoothing Versus Distribution Theory......................... 217
4.3.1 Regression and Conditional Expectation................. 218
4.3.2 Maximum Likelihood Approach........................ 219
4.4 Multiple Regression........................................ 224
4.4.1 Notation............................................ 224
4.4.2 The R Function lm................................... 225
4.4.3 R2 as a Regression Diagnostic......................... 226
4.5 Matrix Formulation and Linear Models........................ 228
4.5.1 Linear Models....................................... 228
4.5.2 Least Squares (Linear) Regression Revisited............. 229
4.5.3 Confidence and Prediction Intervals..................... 235
4.5.4 First Extensions..................................... 236
4.5.5 Testing the CAPM................................... 239
4.6 Polynomial Regression...................................... 243
4.6.1 Polynomial Regression as a Linear Model ............... 243
4.6.2 Example of R Commands............................. 243
4.6.3 Important Remark ................................... 244
4.6.4 Prediction with Polynomial Regression.................. 245
4.6.5 Choice of the Degree p ............................... 248
4.7 Nonlinear Regression....................................... 249
4.7.1 A First Model....................................... 249
4.7.2 Transformation of the Variables........................ 251
4.7.3 A Second Model..................................... 252
4.8 Term Structure of Interest Rates: A Crash Course................ 252
4.8.1 Zero Coupon Bonds.................................. 253
4.8.2 Coupon Bearing Bonds............................... 254
4.8.3 Constructing the Term Structure by Linear Regression? .... 255
4.8.4 Clean Prices Duration.............................. 256
4.8.5 The Three Different Forms of Term Structure............. 257
4.9 Parametric Yield Curve Estimation........................................................258
4.9.1 Estimation Procedures................................................................259
4.9.2 Practical Implementation............................................................260
4.9.3 R Experiments..............................................................................261
4.9.4 Concluding Remarks..................................................................263
Appendix: Cautionary Notes on Some R Idiosyncracies..............................264
Problems...................................................... 268
Notes Complements........................................... 276
5 LOCAL AND NONPARAMETRIC REGRESSION 277
5.1 Review of the Regression Setup .............................. 277
5.2 Basis Expansion Regression.................................. 279
5.2.1 Natural Splines as Local Smoothers..................... 279
5.2.2 Feature Function Expansions.......................... 280
5.3 Nonparametric Scatterplot Smoothers.......................... 283
5.3.1 Smoothing Splines................................... 283
5.3.2 Locally Weighted Regression.......................... 285
5.3.3 A Robust Smoother.................................. 286
5.3.4 The Super Smoother.................................. 287
5.3.5 The Kernel Smoother................................. 287
5.4 More Yield Curve Estimation ................................ 291
5.4.1 A First Estimation Method............................ 291
5.4.2 A Direct Application of Smoothing Splines.............. 292
5.4.3 US and Japanese Instantaneous Forward Rates............ 292
5.5 Multivariate Kernel Regression............................... 293
5.5.1 Running the Kernel in R .............................. 296
5.5.2 An Example Involving the June 1998 S P
Futures Contract..................................... 297
5.6 Projection Pursuit Regression ................................ 303
5.6.1 The R Function ppr.................................. 304
5.6.2 ppr Prediction of the S P Afternoon Indicators.......... 306
5.6.3 More on the Comparison of the Two Methods............ 310
5.7 Nonparametric Option Pricing................................ 311
5.7.1 Nonparametric Pricing Alternatives..................... 311
5.7.2 Description of the Data............................... 312
5.7.3 The Actual Experiment............................... 313
5.7.4 Numerical Results................................... 319
Appendix: Kernel Density Estimation Kernel Regression............ 322
Problems...................................................... 324
Notes Complements........................................... 338
Part III TIME SERIES STATE SPACE MODELS 343
6 TIME SERIES MODELS: AR, MA, ARMA, ALL THAT 345
6.1 Notation and First Definitions................................ 345
6.1.1 Notation............................................ 346
6.1.2 Regular Time Series and Signals ....................... 346
6.1.3 Calendar and Irregular Time Series..................... 348
6.1.4 Creating and Plotting timeSeries Objects in R......... 349
6.1.5 High Frequency Data................................. 349
6.1.6 TimeDate Manipulations............................ 353
6.2 Time Dependent Statistics and Stationarity..................... 355
6.2.1 Statistical Moments.................................. 356
6.2.2 The Notion of Stationarity............................. 356
6.2.3 The Search for Stationarity............................ 361
6.2.4 The Example of the CO2 Concentrations................ 363
6.3 First Examples of Models.................................... 367
6.3.1 White Noise ........................................ 367
6.3.2 Random Walk....................................... 371
6.3.3 Auto Regressive Time Series .......................... 372
6.3.4 Moving Average Time Series.......................... 376
6.3.5 Using the Backward Shift Operator B................... 379
6.3.6 Linear Processes..................................... 380
6.3.7 Causality, Stationarity and Invertibility.................. 381
6.3.8 ARMA Time Series.................................. 385
6.3.9 ARIMA Models..................................... 386
6.4 Fitting Models to Data...................................... 386
6.4.1 Practical Steps....................................... 387
6.4.2 R Implementation.................................... 388
6.5 Putting a Price on Temperature............................... 398
6.5.1 Generalities on Degree Days........................... 398
6.5.2 Temperature Options................................. 399
6.5.3 Statistical Analysis of Temperature Historical Data........ 402
Problems...................................................... 415
Notes Complements........................................... 420
7 MULTIVARIATE TIME SERIES, LINEAR SYSTEMS
AND KALMAN FILTERING 423
7.1 Multivariate Time Series..........................................................................423
7.1.1 Stationarity and Auto-Covariance Functions............................424
7.1.2 Multivariate White Noise............................................................424
7.1.3 Multivariate AR Models............................................................425
7.1.4 Back to Temperature Options....................................................429
7.1.5 Multivariate MA ARIMA Models........................................432
7.1.6 Cointegration..............................................................................433
7.2 State Space Models: Mathematical Set Up............................................435
7.3 Factor Models as Hidden Markov Processes........................................437
7.3.1 Factor Models..............................................................................437
7.3.2 Assumptions of the Model..........................................................438
7.3.3 Dynamics of the Factors............................................................439
7.4 Kalman Filtering of Linear Systems......................................................439
7.4.1 One-Step-Ahead Prediction..................................................440
7.4.2 Derivation of the Recursive Filtering Equations......................440
7.4.3 Filtering........................................................................................444
7.4.4 More Predictions ........................................................................445
7.4.5 Estimation of the Parameters......................................................447
7.5 Applications to Linear Models................................................................448
7.5.1 State Space Representation of Linear Models..........................448
7.5.2 Linear Models with Time Varying Coefficients ......................449
7.5.3 CAPM with Time Varying ß s ..................................................450
7.6 State Space Representation of Time Series............................................453
7.6.1 The Case of AR Series................................................................453
7.6.2 The General Case of ARMA Series.........................455
7.6.3 Fitting ARMA Models by Maximum Likelihood....................456
7.7 Example: Prediction of Quarterly Earnings..................... 457
Problems...................................................... 461
Notes Complements........................................... 471
8 NONLINEAR TIME SERIES: MODELS AND SIMULATION 473
8.1 First Nonlinear Time Series Models........................... 473
8.1.1 Fractional Time Series................................ 474
8.1.2 Nonlinear Auto-Regressive Series...................... 475
8.1.3 Statistical Estimation................................. 476
8.2 More Nonlinear Models: ARCH, G ARCH All That............ 478
8.2.1 Motivation.......................................... 478
8.2.2 ARCH Models...................................... 479
8.2.3 GARCH Models..................................... 481
8.2.4 Summary........................................... 481
8.2.5 R Commands........................................ 482
8.2.6 Fitting a GARCH Model to Real Data................... 483
8.2.7 Generalizations...................................... 493
8.3 Stochastic Volatility Models.................................. 495
8.3.1 Information Structure................................. 495
8.3.2 State Space Formulation.............................. 496
8.3.3 Excess Kurtosis ..................................... 496
8.3.4 Leverage Effect...................................... 497
8.3.5 Comparison with ARCH and GARCH Models............ 498
8.3.6 The Smile Effect..................................... 499
8.4 Discretization of Stochastic Differential Equations..............................500
8.4.1 Discretization Schemes..............................................................501
8.4.2 Monte Carlo Simulations: A First Example..............................503
8.5 Random Simulation and Scenario Generation......................................505
8.5.1 A Simple Model for the S P 500 Index..................................505
8.5.2 Modeling the Short Interest Rate..............................................508
8.5.3 Modeling the Spread..................................................................509
8.5.4 Putting Everything Together......................................................511
8.6 Filtering of Nonlinear Systems..............................................................513
8.6.1 Hidden Markov Models..............................................................513
8.6.2 General Filtering Approach........................................................514
8.6.3 Particle Filter Approximations..................................................515
8.6.4 Filtering in Finance? Statistical Issues......................................519
8.6.5 Application: Tracking Volatility................................................520
Problems............................................................................................................526
Notes Complements......................................................................................531
Part IV BACKGROUND MATERIAL 535
9 APPENDICES 537
9.1 Appendix A: A Quick Introduction to R................................................537
9.1.1 Starting R Under Mac OS, Windows and Under UNIX.... 537
9.1.2 Creating R Objects......................................................................538
9.1.3 Random Generation and White Noise......................................540
9.1.4 More Functions and for Loops................................................542
9.1.5 Importing Data............................................................................544
9.1.6 Programming in R: A First Function........................................549
9.2 Appendix B: A Crash Course on Black-Scholes Option Pricing .... 551
9.2.1 Generalities on Option Pricing..................................................551
Notes Complements......................................................................................558
References 559
Notation Index 565
Data Set Index 569
R Index 571
Author Index 575
Subject Index 579
|
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332/.01/51955 |
| dewey-search | 332/.01/51955 |
| dewey-sort | 3332 11 551955 |
| dewey-tens | 330 - Economics |
| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV041352122 |
| illustrated | Illustrated |
| indexdate | 2024-08-01T10:46:19Z |
| institution | BVB |
| isbn | 9781461487876 9781493938353 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026800675 |
| oclc_num | 871570133 |
| open_access_boolean | |
| owner | DE-521 DE-11 DE-861 DE-523 DE-863 DE-BY-FWS DE-703 |
| owner_facet | DE-521 DE-11 DE-861 DE-523 DE-863 DE-BY-FWS DE-703 |
| physical | xvii, 588 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spellingShingle | Carmona, René 1947- Statistical analysis of financial data in R S-Plus Finances - Modèles mathématiques Finances - Modèles économétriques Finanças (modelos matemáticos) larpcal Matemática financeira larpcal Portfolio-analyse gtt S-Plus gtt Statistische analyse gtt Wiskundige modellen gtt Mathematisches Modell Ökonometrisches Modell Finance Econometric models Finance Mathematical models S-PLUS (DE-588)4321162-8 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| subject_GND | (DE-588)4321162-8 (DE-588)4066472-7 |
| title | Statistical analysis of financial data in R |
| title_auth | Statistical analysis of financial data in R |
| title_exact_search | Statistical analysis of financial data in R |
| title_full | Statistical analysis of financial data in R René A. Carmona |
| title_fullStr | Statistical analysis of financial data in R René A. Carmona |
| title_full_unstemmed | Statistical analysis of financial data in R René A. Carmona |
| title_old | Carmona, René Statistical analysis of financial data in S-PLUS |
| title_short | Statistical analysis of financial data in R |
| title_sort | statistical analysis of financial data in r |
| topic | S-Plus Finances - Modèles mathématiques Finances - Modèles économétriques Finanças (modelos matemáticos) larpcal Matemática financeira larpcal Portfolio-analyse gtt S-Plus gtt Statistische analyse gtt Wiskundige modellen gtt Mathematisches Modell Ökonometrisches Modell Finance Econometric models Finance Mathematical models S-PLUS (DE-588)4321162-8 gnd Wirtschaftsmathematik (DE-588)4066472-7 gnd |
| topic_facet | S-Plus Finances - Modèles mathématiques Finances - Modèles économétriques Finanças (modelos matemáticos) Matemática financeira Portfolio-analyse Statistische analyse Wiskundige modellen Mathematisches Modell Ökonometrisches Modell Finance Econometric models Finance Mathematical models S-PLUS Wirtschaftsmathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026800675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT carmonarene statisticalanalysisoffinancialdatainr |
Inhaltsverzeichnis
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