Optimal statistical inference in financial engineering

Optimal Statistical Inference in Financial Engineering......Page 2
Contents......Page 5
Preface......Page 8
Appendix......Page 352
References......Page 361
CHAPTER 1: Introduction......Page 10
2.1 Probability and Probability Distribution......Page 16
2.2 Vector Random Variable and Independence......Page 26
2.3 Expectation and Conditional Distribution......Page 28
2.4 Convergence and Central Limit Theorems......Page 35
Exercises......Page 39
3.1 Sufficient Statistics......Page 42
3.2 Unbiased Estimators......Page 47
3.3 Efficient Estimators......Page 50
3.4 Asymptotically Efficient Estimators......Page 57
Exercises......Page 62
4.1 Interval Estimation......Page 63
4.2 Most Powerful Test......Page 67
4.3 Various Tests......Page 74
4.4 Discriminant Analysis......Page 77
Exercises......Page 83
5.1 Elements of Stochastic Processes......Page 85
5.2 Spectral Analysis......Page 89
5.3 Ergodicity, Mixing and Martingale......Page 97
5.4 Limit Theorems for Stochastic Processes......Page 101
Exercises......Page 103
CHAPTER 6: Time Series Analysis......Page 105
6.1 Time Series Model......Page 106
6.2 Estimation of Time Series Models......Page 117
6.3 Model Selection Problems......Page 140
6.4 Nonparametric Estimation......Page 149
6.5 Prediction of Time Series......Page 162
6.6 Regression for Time Series......Page 169
6.7 Long Memory Processes......Page 174
6.8 Local Whittle Likelihood Approach......Page 183
6.9 Nonstationary Processes......Page 199
6.10 Semiparametric Estimation......Page 218
6.11 Discriminant Analysis for Time Series......Page 236
Exercises......Page 257
7.1 Option Pricing Theory......Page 259
7.2 Higher Order Asymptotic Option Valuation for Non-Gaussian Dependent Returns......Page 266
7.3 Estimation of Portfolio......Page 284
7.4 VaR Problems......Page 298
Exercises......Page 310
8.1 Spot Rates and Discount Bonds......Page 312
8.2 Estimation Procedures for Term Structure......Page 317
Exercises......Page 323
9.1 Parametric Clustering for Financial Time Series......Page 324
9.2 Nonparametric Clustering for Financial Time Series......Page 332
9.3 Credit Rating Based on Financial Time Series......Page 346
Exercises......Page 351