Machine learning and causal analyses for modeling financial and economic data

Abstract

Instead of aiming at a systematic survey, we consider further developments on several typical linear models and their mixture extensions for prediction modeling, portfolio management and market analyses. The focus is put on outlining the studies by the author’s research group, featured by (a) extensions of AR, ARCH and GARCH models into finite mixture or mixture-of-experts; (b) improvements of Sharpe ratio by maximizing the expected return and the upside volatility while minimizing the downside risk, with the help of a priori aided diversification; (c) developments of arbitrage pricing theory (APT) into temporal factor analysis (TFA)-based temporal APT, macroeconomics-modulated temporal APT and a general formulation for market modeling, together with applications to temporal prediction and dynamic portfolio management; (d) Bayesian Ying–Yang (BYY) harmony learning is adopted to implement these developments, featured with automatic model selection. After a brief introduction on BYY harmony learning, gradient-based algorithms and EM-like algorithms are provided for learning alternative mixture-of-experts-based AR, ARCH and GARCH models; and (e) path analysis for linear causal analyses is briefly reviewed, a recent development on ρ-diagram is refined for cofounder discovery, and a causal potential theory is proposed. Also, further discussions are made on structural equation modeling and its relations to modulated TFA-APT and nGCH-driven M-TFA-O.