1 Introduction 1
2 Elements of Probability 7
2.1 Probability and Probability Distribution 7
2.2 Vector Random Variable and Independence 17
2.3 Expectation and Conditional Distribution 19
2.4 Convergence and Central Limit Theorems 26
Exercises 30
3 Statistical Inference 33
3.1 Sufficient Statistics 33
3.2 Unbiased Estimators 38
3.3 Efficient Estimators 41
3.4 Asymptotically Efficient Estimators 48
Exercises 53
4 Various Statistical Methods 55
4.1 Interval Estimation 55
4.2 Most Powerful Test 59
4.3 Various Tests 66
4.4 Discriminant Analysis 69
Exercises 75

5 Stochastic Processes 77
5.1 Elements of Stochastic Processes 77
5.2 Spectral Analysis 81
5.3 Ergodicity, Mixing and Martingale 89
5.4 Limit Theorems for Stochastic Processes 93
Exercises 95
6 Time Series Analysis 97
6.1 Time Series Model 98
6.2 Estimation of Time Series Models 109
6.3 Model Selection Problems 132
6.4 Nonparametric Estimation 141
6.5 Prediction of Time Series 154
6.6 Regression for Time Series 161
6.7 Long Memory Processes 166
6.8 Local Whittle Likelihood Approach 175
6.9 Nonstationary Processes 191
6.10 Semiparametric Estimation 210
6.11 Discriminant Analysis for Time Series 228
Exercises 249
7 Introduction to Statistical Financial Engineering 251
7.1 Option Pricing Theory 251
7.2 Higher Order Asymptotic Option Valuation for Non-Gaussian
Dependent Returns 258
7.3 Estimation of Portfolio 276
7.4 VaR Problems 290
Exercises 302
8 Term Structure 305
8.1 Spot Rates and Discount Bonds 305
8.2 Estimation Procedures for Term Structure 310
Exercises 316

9 Credit Rating 317
9.1 Parametric Clustering for Financial Time Series 317
9.2 Nonparametric Clustering for Financial Time Series 325
9.3 Credit Rating Based on Financial Time Series 339
Exercises 344
Appendix 345
References 355