Utah State University STOCHASTIC TESTS ON LIVE CATTLE STEER BASIS COMPOSITE FORECASTS by Elliott James Dennis A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in Applied Economics Approved: ____________________ ______________________ Dr. DeeVon Bailey Dr. Dillon Feuz Major Professor Committee Member _____________________ ______________________ Dr. Ryan Bosworth Dr. Man Keun Kim Committee Member Committee Member _____________________ _____________________ Dr. Dale Zobell Dr. Mark McLellan Committee Member Vice President of Research and Dean of School of Graduate Studies UTAH STATE UNIVERSITY Logan, Utah 2014 ii ABSTRACT Stochastic Tests on Live Cattle Steer Basis Composite Forecasts by Elliott James Dennis, Master of Science Utah State University, 2014 Major Professor: Dr. DeeVon Bailey Department: Applied Economics The behavior of basis and the current methods to derive accurate live cattle basis forecasts were examined. The current literature on basis using econometric estimation with an emphasis on composite forecasts in particular was discussed. Mechanical weights of the composite weights were derived using a nonlinear approach. This was supported by a stochastic dominance and efficiency analysis. Considerable support was found for the use of composite basis forecasts in the live cattle industry. Further research should be conducted in the feeder cattle market. (237 pages) iii PUBLIC ABSTRCT Stochastic Tests on Live Cattle Steer Basis Composite Forecasts by Elliott James, Dennis, Master of Science Utah State University, 2014 Major Professor: Dr. DeeVon Bailey Department: Applied Economics Since the seminal papers of Bates and Granger in 1969, a superfluous amount of information has been published on combining singular forecasts. Materialized evidence has habitually demonstrated that combining the forecasts will produce the best model. Moreover, while it is possible that a best singular model could outperform a composite model, using multiple models provides the advantage of risk diversification. It has also been shown to produce a lower forecasting error. The question to whether to combine has been replaced with what amount of emphasis should be placed on each forecast. Researchers are aspired to derive optimal weights that would produce the lowest forecasting errors. An equal composite of the mean square error, by the covariance, and the best previous model, among others, have been suggested. Other academicians have suggested the use of mechanical derived weights through the use of computer programs. These weights have shown robust results. Once the composite and singular forecasts have been estimated, a systematic approach to evaluate the singular forecasts is needed. Forecasting errors, such as the root iv mean square error and mean absolute percentage error, are the most common criteria for elimination in both agriculture and other sectors. Although a valid mean of selection, different forecasting errors can produce a different ordinal ranking of the forecasts; thus, producing inconclusive results. These findings have promoted the inspection for other suitable candidates for forecast evaluation. At the forefront of this pursuit is stochastic dominance and stochastic efficiency. Stochastic dominance and stochastic efficiency have traditionally been used as a way to rank wealth or returns from a group of alternatives. They have been principally used in the finance and money sector as a way to evaluate investment strategies. Holt and Brandt in 1985 proposed using stochastic dominance to select between different hedging strategies. Their results suggest that stochastic dominance has the opportunity to feasibly be used in selecting the most accurate forecast. This thesis had three objectives: 1) To determine whether live cattle basis forecasting error could be reduced in comparison to singular models when using composite forecasts 2) To determine whether stochastic dominance and stochastic efficiency could be used to systematically select the most accurate forecasts 3) To determine whether currently reported forecasting error measures might lead to inaccurate conclusions in which forecast was correct. The objectives were evaluated using two primary markets, Utah and Western Kansas, and two secondary markets, Texas and Nebraska. The data for live cattle slaughter steer basis was taken and subsequently computed from the Livestock Marketing Information Center, Chicago Mercantile Exchange, and United States Department of Agriculture from 2004 to 2012. v Seven singular were initially used and adapted from the current academic literature. After the models were evaluated using forecasting error, stochastic dominance and stochastic efficiency, seven composite models were created. For each separate composite model, a different weighting scheme was applied. The “optimal” composite weight, in particular, was estimated using GAMS whose objective function was to select the forecast combination that would reduce the variance-covariance between the singular forecasting models. The composite models were likewise systematically evaluated using forecasting error, stochastic dominance and stochastic efficiency. The results indicate that forecasting error can be reduced in all four markets, on the average by using an optimal weighting scheme. Optimal weighting schemes can also outperform the benchmark equal weights. Moreover, a combination of fast reaction time series and market condition, supply and demand, forecasts provide the better model. Stochastic dominance and stochastic efficiency provided confirmatory results and selected the efficient set of the forecasts over a range of risk. It likewise indicated that forecasting error may provide a point estimate rather than a range of error. Suggestions for their application and implementation into extension outlook forecasts and industry application are suggested. vi DEDICATION This thesis is dedicated to Dr. DeeVon Bailey. Only through him have I been able to come this far in my education. From the friendly office meetings to stirring intellectual debates, his thoughts and experiences provided me with a solid ground to begin a fruitful career in applied economics. Likewise, it was through his lectures on price analysis that the ideas presented in this paper were formed. No one could ask for a greater beginning. vii ACKNOWLEDGMENTS The ideas that have been generated herein have largely been the product of countless conversations with professors, professionals and fellow students. As such, it has become difficult to ascertain which ideas, if any, can be solely claimed by myself, although I would like to acknowledge Dr. DeeVon Bailey – notably, for creating a suitable environment where my ideas could bud and research could be conducted. Mention should also be given to the members on my committee who helped provided quintessential advice which subsequently, blossomed these ideas. I also need to publicly thank my wife, Tiffany, for her patience and forbearance through the laborious process of working and supporting me all while being pregnant and giving birth to our first daughter, Audrey. Elliott J. Dennis viii CONTENTS Page ABSTRACT ........................................................................................................................ ii PUBLIC ABSTRCT .......................................................................................................... iii DEDICATION ................................................................................................................... vi ACKNOWLEDGMENTS ................................................................................................ vii LIST OF TABLES ............................................................................................................ xii LIST OF FIGURES ......................................................................................................... xvi INTRODUCTION .............................................................................................................. 1 REVIEW OF THE LITERATURE .................................................................................... 6 Current Consensus on Composite Forecasting ........................................................... 6 Theory of Combining .................................................................................................. 8 A Hedge Against Structural Change and Breaks .............................................. 10 Marriage of Forecasts: The Eternal Dilemma ................................................... 11 The Art of Choosing Forecasts: A Methodological Approach ......................... 13 Weights ..................................................................................................................... 14 Other Weighting Methods ................................................................................ 16 Concise Advice on Combining Forecasts ................................................................. 19 Theories that Develop Basis Forecasts ..................................................................... 21 Basis Forecasting Models ......................................................................................... 25 Grain Commodities ........................................................................................... 25 Cattle Basis ....................................................................................................... 26 Composite Basis Models........................................................................................... 30 DATA AND METHODOLOGY ...................................................................................... 32 Weekly Cash ............................................................................................................. 32 Weekly Futures ......................................................................................................... 33 Weekly Basis ............................................................................................................ 34 ix Summary Statistics.................................................................................................... 34 Data Limitations........................................................................................................ 34 Model Identification.................................................................................................. 40 Model #1 – Naive Basis Forecast ..................................................................... 41 Model #2 – Previous Basis Forecast ................................................................. 41 Model #3 – 3-Year Average Forecast ............................................................... 42 Model #4 – Seasonal Trend Forecast ................................................................ 42 Model #5 – Interest Supply Forecast ................................................................ 43 Model #6 – Contract ......................................................................................... 44 Model #7 – Meat Demand ................................................................................ 44 Model Error Identification ........................................................................................ 45 Spearman Rank Correlation .............................................................................. 49 Stochastic Dominance ....................................................................................... 50 Stochastic Efficiency ........................................................................................ 55 Risk Premiums .................................................................................................. 59 Error Measures .......................................................................................................... 61 Categorizing Forecasting Errors ....................................................................... 62 Select Error Measures ....................................................................................... 64 Nonlinear Programming............................................................................................ 67 Parameters Used in the NLP ..................................................................................... 70 Summation to One ............................................................................................ 70 Weights ............................................................................................................. 70 NLP Formulation ...................................................................................................... 71 Scenario 1 – Optimal ........................................................................................ 72 Scenario 2 – Equal ............................................................................................ 72 Scenario 3 – Expert Opinion ............................................................................. 73 Scenario 4 – Ease of use ................................................................................... 73 Scenario 5-7 – Restricted Optimal .................................................................... 74 Procedures ................................................................................................................. 74 Part 1 ................................................................................................................. 75 Part 2 ................................................................................................................. 75 Part 3 ................................................................................................................. 77