Statistical Portfolio Estimation

Cover -- Half Title -- Title -- Copyright -- Contents -- Preface -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1 Stochastic Processes and Limit Theorems -- Chapter 3. Portfolio Theory for Dependent Return Processes -- 3.1 Introduction to Portfolio Theory -- 3.1.1 Mean-Variance Portfolio -- 3.1.2 Capital Asset Pricing Model -- 3.1.3 Arbitrage Pricing Theory -- 3.1.4 Expected Utility Theory -- 3.1.5 Alternative Risk Measures -- 3.1.6 Copulas and Dependence -- 3.1.7 Bibliographic Notes -- 3.1.8 Appendix -- 3.2 Statistical Estimation for Portfolios -- 3.2.1 Traditional Mean-Variance Portfolio Estimators -- 3.2.2 Pessimistic Portfolio -- 3.2.3 Shrinkage Estimators -- 3.2.4 Bayesian Estimation -- 3.2.5 Factor Models -- 3.2.5.1 Static factor models -- 3.2.5.2 Dynamic factor models -- 3.2.6 High-Dimensional Problems -- 3.2.6.1 The case of m/n . y . (0, 1 -- 3.2.6.2 The case of m/n . y . (1,8 -- 3.2.7 Bibliographic Notes -- 3.2.8 Appendix -- 3.3 Simulation Results -- 3.3.1 Quasi-Maximum Likelihood Estimator -- 3.3.2 Efficient Frontier -- 3.3.3 Difference between the True Point and the Estimated Point -- 3.3.4 Inference of µP -- 3.3.5 Inference of Coefficient -- 3.3.6 Bibliographic Notes -- Chapter 4. Multiperiod Problem for Portfolio Theory -- 4.1 Discrete Time Problem -- 4.1.1 Optimal PortfolioWeights -- 4.1.2 Consumption Investment -- 4.1.3 Simulation Approach for VAR(1) model -- 4.1.4 Bibliographic Notes -- 4.2 Continuous Time Problem -- 4.2.1 Optimal Consumption and PortfolioWeights -- 4.2.2 Estimation -- 4.2.2.1 Generalized method of moments (GMM -- 4.2.2.2 Threshold estimation method -- 4.2.3 Bibliographic Notes -- 4.3 Universal Portfolio -- 4.3.1 µ-Weighted Universal Portfolios -- 4.3.2 Universal Portfolios with Side Information -- 4.3.3 Successive Constant Rebalanced Portfolios

4.3.4 Universal Portfolios with Transaction Costs -- 4.3.5 Bibliographic Notes -- 4.3.6 Appendix -- Chapter 5. Portfolio Estimation Based on Rank Statistics -- 5.1 Introduction to Rank-Based Statisticsrank -- 5.1.1 History of Ranks -- 5.1.1.1 Wilcoxon's signed rank and rank sum tests -- 5.1.1.2 Hodges-Lehmann and Chernoff-Savage -- 5.1.2 Maximal Invariantsmaximal invariant -- 5.1.2.1 Invariance of sample space, parameter space and tests -- 5.1.2.2 Most powerful invariant testmost powerful invariant test -- 5.1.3 Efficiencyefficiency of Rank-Based Statistics -- 5.1.3.1 Least favourableleast favourable density and most powerfulmost powerful test -- 5.1.3.2 Asymptotically most powerful rank test -- 5.1.4 U-Statistics for Stationary Processes -- 5.2 Semiparametrically Efficient Estimation in Time Series -- 5.2.1 Introduction to Rank-Based Theory in Time Series -- 5.2.1.1 Testing for randomness against ARMA alternatives -- 5.2.1.2 Testing an ARMA model against other ARMA alternatives -- 5.2.2 Tangent Spacetangent space -- 5.2.3 Introduction to Semiparametric Asymptotic Optimal Theory -- 5.2.4 Semiparametrically Efficient Estimation in Time Series, and Multivariate Cases -- 5.2.4.1 Rank-based optimal influence functions (univariate case -- 5.2.4.2 Rank-based optimal estimation for elliptical residuals -- 5.3 Asymptotic Theory of Rank Order Statistics for ARCH Residual Empirical Processes -- 5.4 Independent Component Analysis -- 5.4.1 Introduction to Independent Component Analysis -- 5.4.1.1 The foregoing model for financial time series -- 5.4.1.2 ICA modeling for financial time series -- 5.4.1.3 ICA modeling in frequency domain for time series -- 5.5 Rank-Based Optimal Portfolio Estimation -- 5.5.1 Portfolio Estimation Based on Ranks for Independent Components

5.5.2 Portfolio Estimation Based on Ranks for Elliptical Residualselliptical residuals -- Chapter 6. Portfolio Estimation Influenced by Non-Gaussian Innovations and Exogenous Variables -- Chapter 6 .1 Robust Portfolio Estimation under Skew-Normal Return Processes -- 6.2 Portfolio Estimators Depending on Higher-Order Cumulant Spectra -- 6.3 Portfolio Estimation under the Utility Function Depending on Exogenous Variables -- 6.4 Multi-Step Ahead Portfolio Estimation -- 6.5 Causality Analysis -- 6.6 Classificationclassification by Quantile Regressionquantile regression -- 6.7 Portfolio Estimation under Causal Variables -- Chapter 7. Numerical Examples -- 7.1 Real Data Analysis for Portfolio Estimation -- 7.1.1 Introduction -- 7.1.2 Data -- 7.1.3 Method -- 7.1.3.1 Model selection -- 7.1.3.2 Confidence region -- 7.1.3.3 Locally stationary estimation -- 7.1.4 Results and Discussion -- 7.1.5 Conclusions -- 7.1.6 Bibliographic Notes -- 7.2 Application for Pension Investment -- 7.2.1 Introduction -- 7.2.2 Data -- 7.2.3 Method -- 7.2.4 Results and Discussion -- 7.2.5 Conclusions -- 7.3 Microarray Analysis Using Rank Order Statistics for ARCH Residual -- 7.3.1 Introduction -- 7.3.2 Data -- 7.3.3 Method -- 7.3.3.1 The rank order statistic for the ARCH residual empirical process -- 7.3.3.2 Two-group comparison for microarray data -- 7.3.3.3 GO analysis -- 7.3.3.4 Pathway analysis -- 7.3.4 Simulation Study -- 7.3.5 Results and Discussion -- 7.3.5.1 Simulation data -- 7.3.5.2 Affy947 expression dataset -- 7.3.6 Conclusions -- 7.4 Portfolio Estimation for Spectral Density of Categorical Time Series Data -- 7.4.1 Introduction -- 7.4.2 Method -- 7.4.2.1 Spectral Envelope -- 7.4.2.2 Diversification analysis

7.4.2.3 An extension of SpecEnv to the mean-diversification efficient frontier -- 7.4.3 Data -- 7.4.3.1 Simulation data -- 7.4.3.2 DNA sequence data -- 7.4.4 Results and Discussion -- 7.4.4.1 Simulation study -- 7.4.4.2 DNA sequence for the BNRF1 genes -- 7.4.5 Conclusions -- 7.5 Application to Real-Value Time Series Data for Corticomuscular Functional Coupling for SpecEnv and the Portfolio Study -- 7.5.1 Introduction -- 7.5.2 Method -- 7.5.3 Results and Discussion -- Chapter 8. Theoretical Foundations and Technicalities -- 8.1 Limit Theorems for Stochastic Processes -- 8.2 Statistical Asymptotic Theory -- 8.3 Statistical Optimal Theory -- 8.4 Statistical Model Selection -- 8.5 Efficient Estimation for Portfolios -- 8.5.1 Traditional mean variance portfolio estimators -- 8.5.2 Efficient mean variance portfolio estimators -- 8.5.3 Appendix -- 8.6 Shrinkage Estimation -- 8.7 Shrinkage Interpolation for Stationary Processes -- Bibliography -- Author Index -- Subject Index