BYY harmony learning, independent state space, and generalized APT financial analyses

First, the relationship between factor analysis (FA) and the well-known arb itrage pricing theory (APT) for financial market has been discussed compara tively, with a number of to-be-improved problems listed. An overview has be en made from a unified perspective on the related studies in the literature s of statistics, control theory, signal processing, and neural networks. Se cond, we introduce the fundamentals of the Bayesian Ying Yang (BYY) system and the harmony learning principle which has been systematically developed in past several years as a unified statistical framework for parameter lear ning, regularization and model selection, in both nontemporal and temporal stochastic environments. We further show that a specific case of the framew ork, called BYY independent state space (ISS) system, provides a general gu ide for systematically tackling various FA related learning tasks and the a bove to-be-improved problems for the APT analyses. Third, on various specif ic cases of the BYY ISS system in three typical architectures, adaptive alg orithms, regularization methods and model selection criteria are provided f or either or both of parameter learning with automated model selection and parameter learning followed by model selection. In the B-architectures, new results are provided for Gaussian and non-Gaussian FA, binary FA, independ ent Hidden Markov Model (HMM) and Temporal FA, as well as other extensions, which are then applied to statistical APT analyses for solving the above t o-be-improved problems. In the F-architectures, adaptive algorithms are giv en for several extensions of independent component analysis (ICA), includin g competitive ICA, Gaussian and non-Gaussian temporal ICA. Moreover, the ad vantages of the B-architectures and the F-architectures are traded off in t he BI-architectures, not only with new strength to the existing least mean square error reconstruction (LMSER) learning, hut also with various LMSER e xtensions, including the so-called principal ICA and its temporal extension . The final part of this paper introduces some other financial applications that base on the underlying independent factors via the APT analyses, incl uding prediction of macroeconomic indexes, portfolio management hy adaptive ly maximizing an adjusted Shape ratio, and a macroeconomics modulated indep endent state-space model for financial market modeling.