Hector O. Zapata

This article compares ARMA-GARCH models under alternative statistical distributions to identify the best fit for risk assessment in selected U.S. agricultural commodity markets. The Kupiec proportion-of-failures test assesses whether actual losses exceed expected losses from each model for rice, soybeans, wheat, corn, cotton, orange juice and live cattle in daily futures prices from 1994 to 2026. In sample, ARMA-eGARCH models with skewed Student-t innovations have the lowest AIC and give correct 5% Value-at-Risk coverage for all seven commodities, whereas models with normal innovations are rejected for five of the seven. Out of sample (March 2020 to June 2026), the selected models pass the Kupiec test in 26 of 28 cases, while a normal GARCH(1,1) produces too many violations at the 1% level. A GARCH(1,1) with skewed Student-t innovations forecasts Value-at-Risk about as well as the selected models, so the distributional assumption, rather than the complexity of the volatility equation, accounts for most of the gain in accuracy. The study finds, similarly to other studies, that the skewed Student-t distribution works best in fitting kurtosis and skewness for risk analysis purposes.

A four-parameter Generalized Lambda Distribution (GLD) quantile regression is applied to a standard capital asset pricing model (CAPM) error specification to jointly estimate moments of the residuals using the daily prices of two farmland Real Estate Investment Trusts (REITs), Nasdaq: LAND and NYSE: FPI as a function of the U.S. S&P 500 from April 2014 to August 2024. The GLD regression also captures the effect of outliers found in the OLS CAPM model, resulting in a closer fit to the theoretical distribution of the GLD residuals. Simulation results revealed symmetrically distributed CAPM coefficients of farmland REITs. The findings suggest that LAND and FPI do not offer portfolio diversification beyond that provided by a market index such as the S&P 500. While the numerical magnitude of the estimated coefficients from the GLD regression is identical to those of least squares, the GLD estimates are more accurate and robust to outliers and more consistent with the distributional properties of daily returns. Future research with this relatively new regression method is briefly discussed.

Considerable studies have examined the relationship between commodity markets and stock markets. This paper studies the cyclical relationship between commodity markets and stock markets with implications for investing based on index relationships. Stock markets are represented by the U.S. S&P 500 index and aggregate commodity markets by the U.S. producer price index (PPI). Tradeable market indexes readily available to investors, namely the S&P GSCI Index and the Bloomberg Commodity Index (BCOM), are also studied. An optimal bandpass filter is used to estimate the cyclical component using a pricing-performance measure of the S&P 500 relative to the PPI, based on annual data from 1871 to 2022. The S&P GSCI and the BCOM indexes are also used to test the robustness of the findings. The impacts of the financial crisis of 2008 and the coronavirus pandemic are also assessed. The overriding conclusion of the study is that a cyclical relationship exists between stock markets and commodity markets for both aggregate and tradeable indexes which can last, from peak to peak, approximately 31 years. Measuring returns and risks in a manner consistent with these cycles can shed new light on the usefulness of commodity investing via tradeable indexes in seeking efficient portfolios.

Machine learning (ML) is a novel method that has applications in asset pricing and that fits well within the problem of measurement in economics. Unlike econometrics, ML models are not designed for parameter estimation and inference, but similar to econometrics, they address, and may be better suited for, problems of prediction. While some ML methods have been applied in econometrics for decades, their success in prediction has been limited, and examples of this abound in the asset pricing literature. In recent years, the ML literature has advanced new, more efficient, computation methods for regularization, modeling nonlinearity, and improved out-of-sample prediction. This article conducted a comprehensive, objective, and quantitative bibliometric analysis of this growing literature using Web of Science (WoS) data. We identified trends in the literature over the past decade, the geographical distribution of articles, authorship, and institutional contributions worldwide. The paper also identifies the dominant literature using citations in WoS and discusses computational algorithms that are expanding the econometric frontiers in asset pricing. The top cited papers were reviewed, highlighting their contribution. The limitations of ML learning methods and recent advances in ML were used to provide a conic view to future ML econometric practice.