Machine learning and causal analyses for modeling financial and economic data

Lei Xu

doi:10.1186/s40535-018-0058-5

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.

Highlights

Financial and economic data are naturally recorded as temporal sequences or time series, and one of major tasks on those data is making time series analysis
One most classic tool for time series analyses is the autoregressive (AR) model or generally autoregressive–moving-average (ARMA) model, which describes a linear dependence of the current observation on past values and noise disturbances
Further developments of these linear models introduced are suggested to be implemented by the Bayesian Ying–Yang (BYY) harmony learning

Summary

Introduction

Financial and economic data are naturally recorded as temporal sequences or time series, and one of major tasks on those data is making time series analysis. Further developments of these linear models introduced are suggested to be implemented by the Bayesian Ying–Yang (BYY) harmony learning. (i) for HMM mixture by Eq(8), ln[qjt |jt−1 q(xqt−1|ψjt )G(xt − μjt ,t |0, σj2t,t )], (ii) for HMM AME by Eq(15) Another stream of automatic model selection is featured by those appropriate priorbased efforts. Dirichlet–Normal–Wishart priories is added on Gaussian components in the implementation of the variational Bayes (VB) that computes a lower bound of the marginal likelihood (McGrory and Titterington 2007) These efforts highly depend on choosing an appropriate prior, which is usually a difficult task, while an inappropriate prior may deteriorate the performance of model selection seriously. Yang harmony learning and two exemplar learning algorithms” section, where a tutorial is provided on one BYY harmony learning algorithm for alternative mixture-ofexperts-based GARCH models

Dynamic trading and portfolio management

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Linear causal analyses

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