## 3 Research Design
### Data Selection and Description  
As mentioned in the first section, in order to make comparison of the forecasting performance among different models, our study chooses three agricultural commodity futures prices--namely the wheat, corn and soybean--to conduct empirical research. The original data of these three futures prices are obtained from the Chicago Board of Trade (CBOT), which is available on the CME Group's website ([[http://www.cmegroup.com/](http://www.cmegroup.com/)]([http://www.cmegroup.com/](http://www.cmegroup.com/))). The reasons why we take these three agricultural commodity futures prices as research objects are as follows: (1) CME Group is the world's leading and most diverse derivatives marketplace, and how its futures prices change usually does have a great effect on other countries' futures markets, which certainly includes wheat, corn and soybean futures; (2) these agricultural commodities feed a large part of the world's population directly or indirectly [15], which will strengthen the interplay between food grain futures prices and its supply-demand situation to some extent; and (3) corn, wheat and soybean play an extremely important role in the world's three leading economics which are the United States, the European Union and China, respectively, in the aspect of consuming and importing.  
More specifically, we choose these three commodities' closing prices of continuous futures contracts as sample data in our study, which are daily data with the same sample size (1500 observations) but covering different periods, shown in Table 1. Note that the wheat futures explicitly represent the Chicago SRW wheat futures, since its average daily volume (ADV) is larger than other wheat futures based on the CME Group's leading products reports. Meanwhile, for each sample data of wheat, corn and soybean, the first 1200 observations (80%) are taken as the training set of models proposed above, while the last 20% (300 observations) is treated as the testing set (See Table 1). In the process of forecasting each dataset, the PSO-BPNN is trained by the training set corresponding to the dataset, and after this, the study uses the testing set to evaluate and compare the forecasting performance of all hybrid models presented in this paper.  
Figure 4 gives the sequence chart of the daily futures prices of wheat, corn and soybean. It can be seen from this figure that the soybean futures prices keep at a higher level than other two futures during the whole period, while the corn futures prices are a little lower than the prices of wheat in most of this period. Although prices of these three futures differ from each other, they approximately have their movement trend in common. Furthermore, all three futures price time series, which are nonlinear and nonstationary in nature, show the characteristics of relatively large fluctuation, which can help the decomposition methods to well exert the role of data pretreatment.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Futures** & **Period** & **Sample Size** & **Training Set** & **Testing Set** \\ \hline Corn & 13 August 2010 to 29 July 2016 & 1500 & 1200 & 300 \\ Soybean & 10 August 2010 to 29 July 2016 & 1500 & 1200 & 300 \\ Wheat & 13 August 2010 to 29 July 2016 & 1500 & 1200 & 300 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Period and length of the three futures prices.