## 2 Problem Statement and Data Analysis
### Data Analysis  
Commodity contracts for paired transactions often need to have a long-term and stable cointegration relationship, such as the combination of rebar and hot-rolled coil. This paper makes a prediction study based on the real price difference data of this combination. This section demonstrates the effectiveness of using data. To ascertain the presence of a long-term stable cointegration relationship among the selected futures contracts, we utilized EViews10 software to conduct a cointegration analysis on the original price data. A close examination of the contract time series plot shown in Figure 1 reveals that the closing price data for both RB and HC display comparable fluctuation patterns. This initial observation indicates a potential correlation between the price data of these two commodity futures. A comprehensive quantitative analysis of this correlation is furnished in Table 1. The correlation coefficients computed for the opening price, closing price, highest price, and lowest price collectively suggest a significant correlation between the two commodities. \begin{table}
\begin{tabular}{c c c c c} \hline
**CORR** & **Open** & **Close** & **High** & **Low** \\ \hline RB-HC & 0.990999 & 0.991001 & 0.991005 & 0.990997 \\ \hline \end{tabular}  
A correlation analysis of two time series, RB and HC, was conducted based on tick data and fitted into 1 min candlesticks where four price indicators are correspondingly analyzed for correlation.  
\end{table} 
Table 1: Correlation test of the time series. Figure 1: Time series plot of the closing prices for RB and HC. While most variables within financial data are nonstationary, research into their correlations reveals intrinsic linkages and a stable equilibrium relationship over the long term. In this study, we performed stationarity tests on the selected RB and RH price series, employing the commonly used augmented Engle-Granger (ADF) method to test the stationarity of the time series. Tests were conducted for the series at 0 th and 1 st order unit root, with results presented in Table 2. As the data in the table elucidate, for the price series of RB and HC, we could not reject the null hypothesis at a 5% confidence level in the 0-order unit root test. Therefore, all variables were nonstationary. However, after differentiating the series at the 1 st order, the absolute values of the t-statistics of each variable were greater than any critical value, with accompanying probabilities of zero, indicating each of them was stationary under a first-order differential. Consequently, it can be inferred that the price series of the principal futures contracts of both RB and HC are integrated into order one. Subsequently, we can initiate the Engle-Granger cointegration test, beginning with the formulation of the cointegration equation as follows:  
\[hc\_close=c\cdot rb\_close+et \tag{2}\]  
where \(et\) denotes the cointegration residual, or simply the residual. The parameter \(c\) represents the cointegration coefficient. Table 3 presents the results of the Engle-Granger cointegration test. At the 1% confidence level, the ADF test statistic of the residual series is smaller than the critical value. As a result, we reject the null hypothesis and consider the series to be stationary. In accordance with [PERSON]'s cointegration theory, we deduce that the price data for the main contracts of RB and HC exhibit a cointegration relationship. Consequently, these data are suitable for pair trading.