This paper introduces methodologies in forecasting oil prices (Brent and WTI) with multivariate time series of major S&P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. We also apply Bayesian variable selection and nonlinear principal component analysis (NLPCA) for data dimension reduction. With a reduced number of important covariates, we also forecast oil prices (Brent and WTI) with multivariate time series of major S&P 500 stock prices using Gaussian process modeling, deep learning, and vine copula regression. To apply real data to the proposed methods, we select monthly log returns of 2 oil prices and 74 large-cap, major S&P 500 stock prices across the period of February 2001–October 2019. We conclude that vine copula regression with NLPCA is superior overall to other proposed methods in terms of the measures of prediction errors.

The study of a causal interpretation of board and firm characteristics, that is, a hidden dependence relationship on the causal inference among board and firm characteristics, is an important but unaddressed issue in the corporate governance literature. Using diverse advanced statistical methods and focusing on Tobin’s Q, we find that (i) not all board variables previously found to be significant are “robust” to latent variable data analysis, and (ii) those variables that are consistently significant differ markedly in latent structural equation analysis. Our analyses provide researchers interested in board issues with an important caveat: Focusing on the dependence structure of available board variables affected by latent factors may introduce a new horizon in corporate finance.