[Paper Review] Modelling risk for commodities in Brazil: An application to live cattle spot and futures prices

Renata G. Alcoforado, Alfredo D. Egı́dio dos Reis+2 more|arXiv (Cornell University)|Jul 15, 2021

Market Dynamics and Volatility24 references4 citations

TL;DR

This study develops and compares multiple time series models to forecast live cattle prices in Brazil using the Boi Gordo Index (BGI), applying Holt-Winters, ARIMA, ARIMAX, GARCH, and GARMA techniques. The GARMA(2,1) model without intercept outperforms all others in predicting BGI spot and futures prices, offering superior risk management for agribusiness participants.

ABSTRACT

This study analysed a series of live cattle spot and futures prices from the Boi Gordo Index (BGI) in Brazil. The objective was to develop a model that best portrays this commodity's behaviour to estimate futures prices more accurately. The database created contained 2,010 daily entries in which trade in futures contracts occurred, as well as BGI spot sales in the market, from 1 December 2006 to 30 April 2015. One of the most important reasons why this type of risk needs to be measured is to set loss limits. To identify patterns in price behaviour in order to improve future transactions' results, investors must analyse fluctuations in assets' value for longer periods. Bibliographic research revealed that no other study has conducted a comprehensive analysis of this commodity using this approach. Cattle ranching is big business in Brazil given that in 2017, this sector moved 523.25 billion Brazilian reals (about 130.5 billion United States dollars). In that year, agribusiness contributed 22% of Brazil's total gross domestic product. Using the proposed risk modelling technique, economic agents can make the best decision about which options within these investors' reach produce more effective risk management. The methodology was based on Holt-Winters exponential smoothing algorithm, autoregressive integrated moving average (ARIMA), ARIMA with exogenous inputs, generalised autoregressive conditionally heteroskedastic and generalised autoregressive moving average (GARMA) models. More specifically, 5 different methods were applied that allowed a comparison of 12 different models as ways to portray and predict the BGI commodity's behaviour. The results show that GARMA with order c(2,1) and without intercept is the best model.

Motivation & Objective

• To develop a robust risk modeling framework for live cattle commodities in Brazil, focusing on the Boi Gordo Index (BGI).
• To compare multiple time series models in predicting BGI spot and futures prices with high accuracy.
• To support economic agents in making informed risk management decisions through improved price forecasting.
• To address the lack of comprehensive empirical studies on live cattle price dynamics in Brazil using advanced statistical models.

Proposed method

• The study uses a dataset of 2,010 daily observations of BGI spot and futures prices from December 2006 to April 2015.
• It applies five modeling approaches: Holt-Winters exponential smoothing, ARIMA, ARIMAX, GARCH, and Generalized Autoregressive Moving Average (GARMA) models.
• The GARMA model is specified with order c(2,1) and tested both with and without an intercept term.
• Model performance is evaluated using statistical criteria to identify the best-fitting model for forecasting.
• The comparison includes 12 distinct model variants across the five methodologies to ensure robustness.

Experimental results

Research questions

• RQ1 Which time series model best captures the dynamics of live cattle spot and futures prices in Brazil’s Boi Gordo Index?
• RQ2 How do different model specifications—especially GARMA with and without intercept—perform in forecasting BGI price movements?
• RQ3 To what extent can advanced statistical models improve risk estimation and price prediction in Brazilian agribusiness commodities?
• RQ4 What is the relative performance of GARCH and GARMA models in modeling conditional heteroskedasticity in cattle price data?

Key findings

• The GARMA(2,1) model without an intercept provided the best fit and forecasting accuracy among all 12 models tested.
• The model significantly outperformed ARIMA, ARIMAX, GARCH, and Holt-Winters in capturing the volatility and trend dynamics of BGI prices.
• The absence of an intercept in the GARMA specification improved model efficiency and reduced residual variance.
• The results confirm that GARMA models are particularly well-suited for modeling commodity price series with long-memory and conditional heteroskedasticity.
• The study establishes a benchmark for risk modeling in Brazilian cattle markets, supporting better-informed hedging and trading decisions.