System Theoretic Time-Series Forecasts of Weekly Live Cattle Prices

Multivariate time-series forecasts of weekly live cattle prices in six different geographic markets are developed using a procedure based on the principles of linear systems theory. These forecasts were found to be informative and superior to those obtained from an alternative model. Following the approach developed for stock prices by Cerchi and Havenner, arbitrage portfolios were constructed from the model parameters. A simulation exercise based on 208 weekly observations withheld from model specification and estimation suggests that these arbitrage activities would have been profitable in practice. Key words: cattle prices, forecasting, multivariate time series. The economics of beef production is such that optimum growth per input is attained after ap-proximately six months of confined feeding. When market conditions dictate, cattle can be fed to heavier weights and still make choice grade or sold lighter to increase current market supplies, but the flexibility is limited to a mar-keting window approximately six weeks long. Our objective in this paper is to provide guid-ance to cattle market participants by providing accurate short-run price forecasts to aid the selling decision. We do this by fitting a multi-variate time-series model to 531 weekly obser-vations of seven live cattle prices. As we shall see in the following sections, these series are so tightly interrelated that it is necessary to model them all jointly in a large system. The large number of series results in implied univariate polynomials in the lag operator of large order, even for small lags in the integrated matrix lag polynomial of the system; thus the dynamics are complex, and it is difficult to determine valid restrictions on the model to reduce sam-pling error in the forecasts. We use a procedure by Aoki grounded in linear systems theory t