Independent factor model constructions and its applications in finance.

by Siu-ming Cha.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 123-132).Abstracts in English and Chinese.Abstract --- p.iAcknowledgements --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Objective --- p.1Chapter 1.2 --- Problem --- p.1Chapter 1.2.1 --- Motivation --- p.1Chapter 1.2.2 --- Approaches --- p.3Chapter 1.3 --- Contributions --- p.4Chapter 1.4 --- Organization of this Thesis --- p.5Chapter 2 --- Independent Component Analysis --- p.8Chapter 2.1 --- Overview --- p.8Chapter 2.2 --- The Blind Source Separation Problem --- p.8Chapter 2.3 --- Statistical Independence --- p.10Chapter 2.3.1 --- Definition --- p.10Chapter 2.3.2 --- Measuring Independence --- p.11Chapter 2.4 --- Developments of ICA Algorithms --- p.15Chapter 2.4.1 --- ICA Algorithm: Removal of Higher Order Dependence --- p.16Chapter 2.4.2 --- Assumptions in ICA Algorithms --- p.19Chapter 2.4.3 --- Joint Approximate Diagonalization of Eigenmatrices(JADE) --- p.20Chapter 2.4.4 --- Fast Fixed Point Algorithm for Independent Component Analysis(FastICA) --- p.21Chapter 2.5 --- Principal Component Analysis and Independent Component Anal- ysis --- p.23Chapter 2.5.1 --- Theoretical Comparisons between ICA and PCA --- p.23Chapter 2.5.2 --- Comparisons between ICA and PCA through a Simple Example --- p.24Chapter 2.6 --- Applications of ICA in Finance: A review --- p.27Chapter 2.6.1 --- Relationships between Cocktail-Party Problem and Fi- nance --- p.27Chapter 2.6.2 --- Security Structures Explorations --- p.28Chapter 2.6.3 --- Factors Interpretation and Visual Analysis --- p.29Chapter 2.6.4 --- Time Series Prediction by Factors --- p.29Chapter 2.7 --- Conclusions --- p.30Chapter 3 --- Factor Models in Finance --- p.31Chapter 3.1 --- Overview --- p.31Chapter 3.2 --- Factor Models and Return Generating Processes --- p.32Chapter 3.2.1 --- One-Factor Model --- p.33Chapter 3.2.2 --- Multiple-Factor Model --- p.34Chapter 3.3 --- Abstraction of Factor Models in Portfolio --- p.35Chapter 3.4 --- Typical Applications of Factor Models: Portfolio Mangement --- p.37Chapter 3.5 --- Different Approaches to Estimate Factor Model --- p.39Chapter 3.5.1 --- Time-Series Approach --- p.39Chapter 3.5.2 --- Cross-Section Approach --- p.40Chapter 3.5.3 --- Factor-Analytic Approach --- p.41Chapter 3.6 --- Conclusions --- p.42Chapter 4 --- ICA and Factor Models --- p.43Chapter 4.1 --- Overview --- p.43Chapter 4.2 --- Relationships between BSS and Factor Models --- p.43Chapter 4.2.1 --- Mathematical Deviation from Factor Models to Mixing Process --- p.45Chapter 4.3 --- Procedures of Factor Model Constructions by ICA --- p.47Chapter 4.4 --- Sorting Criteria for Factors --- p.48Chapter 4.4.1 --- Kurtosis --- p.50Chapter 4.4.2 --- Number of Runs --- p.52Chapter 4.5 --- Experiments and Results I: Factor Model Constructions --- p.53Chapter 4.5.1 --- Factors and their Sensitivities Extracted by ICA --- p.55Chapter 4.5.2 --- Factor Model Construction for a Stock --- p.60Chapter 4.6 --- Discussion --- p.62Chapter 4.6.1 --- Remarks on Applying ICA to Find Factors --- p.62Chapter 4.6.2 --- Independent Factors and Sparse Coding --- p.63Chapter 4.6.3 --- Selecting Securities for ICA --- p.63Chapter 4.6.4 --- Factors in Factor Models --- p.65Chapter 4.7 --- Conclusions --- p.66Chapter 5 --- Factor Model Evaluations and Selections --- p.67Chapter 5.1 --- Overview --- p.67Chapter 5.2 --- Random Residue: Requirement of Independent Factor Model --- p.68Chapter 5.2.1 --- Runs Test --- p.68Chapter 5.2.2 --- Interpretation of z-value --- p.70Chapter 5.3 --- Experiments and Results II: Factor Model Selections --- p.71Chapter 5.3.1 --- Randomness of Residues using Different Sorting Criteria --- p.71Chapter 5.3.2 --- Reverse Sortings of Kurtosis and Number of Runs --- p.76Chapter 5.4 --- Experiments and Results using FastICA --- p.80Chapter 5.5 --- Other Evaluation Criteria for Independent Factor Models --- p.85Chapter 5.5.1 --- Reconstruction Error --- p.86Chapter 5.5.2 --- Minimum Description Length --- p.89Chapter 5.6 --- Conclusions --- p.92Chapter 6 --- New Applications of Independent Factor Models --- p.93Chapter 6.1 --- Overview --- p.93Chapter 6.2 --- Applications to Financial Trading System --- p.93Chapter 6.2.1 --- Modifying Shocks in Stocks --- p.96Chapter 6.2.2 --- Modifying Sensitivity to Residue --- p.100Chapter 6.3 --- Maximization of Higher Moment Utility Function --- p.104Chapter 6.3.1 --- No Good Approximation to Utility Function --- p.107Chapter 6.3.2 --- Uncorrelated and Independent Factors in Utility Ma mizationxi- --- p.108Chapter 6.4 --- Conclusions --- p.110Chapter 7 --- Future Works --- p.111Chapter 8 --- Conclusion --- p.113Chapter A --- Stocks used in experiments --- p.116Chapter B --- Proof for independent factors outperform dependent factors in prediction --- p.117Chapter C --- Demixing Matrix and Mixing Matrix Found by JADE --- p.119Chapter D --- Moments and Cumulants --- p.120Chapter D.1 --- Moments --- p.120Chapter D.2 --- Cumulants --- p.121Chapter D.3 --- Cross-Cumulants --- p.121Bibliography --- p.12

Extraction of the underlying structure of systematic risk from non-Gaussian multivariate financial time series using independent component analysis: Evidence from the Mexican stock exchange

Regarding the problems related to multivariate non-Gaussianity of financial time series, i.e., unreliable results in extraction of underlying risk factors -via Principal Component Analysis or Factor Analysis-, we use Independent Component Analysis (ICA) to estimate the pervasive risk factors that explain the returns on stocks in the Mexican Stock Exchange. The extracted systematic risk factors are considered within a statistical definition of the Arbitrage Pricing Theory (APT), which is tested by means of a two-stage econometric methodology. Using the extracted factors, we find evidence of a suitable estimation via ICA and some results in favor of the APT.Peer ReviewedPostprint (published version

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