Optimal statistical inference in financial engineering

Masanobu Taniguchi, Junichi Hirukawa, Kenichiro Tamaki1584885912, 9781584885917, 9781420011036

Until now, few systematic studies of optimal statistical inference for stochastic processes had existed in the financial engineering literature, even though this idea is fundamental to the field. Balancing statistical theory with data analysis, Optimal Statistical Inference in Financial Engineering examines how stochastic models can effectively describe actual financial data and illustrates how to properly estimate the proposed models. After explaining the elements of probability and statistical inference for independent observations, the book discusses the testing hypothesis and discriminant analysis for independent observations. It then explores stochastic processes, many famous time series models, their asymptotically optimal inference, and the problem of prediction, followed by a chapter on statistical financial engineering that addresses option pricing theory, the statistical estimation for portfolio coefficients, and value-at-risk (VaR) problems via residual empirical return processes. The final chapters present some models for interest rates and discount bonds, discuss their no-arbitrage pricing theory, investigate problems of credit rating, and illustrate the clustering of stock returns in both the New York and Tokyo Stock Exchanges. Basing results on a modern, unified optimal inference approach for various time series models, this reference underlines the importance of stochastic models in the area of financial engineering.

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Table of contents :
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