## 4 Applied Methods
### Classification and Regression Tree (CART)  
The decision tree (DT) is one of the non-parametrical approaches for classification purposes. In this approach, a model of classification is introduced for available observation using a very simple technique. The introduced model has a very simple structure, and is comprehensible for decision-making. Although this approach uses simple techniques, it can be performed even sometimes better than complicated approaches such as ANN [88]. The DT has a graph the same as a tree and is composed of roots, branches, leaves, and nodes [65; 89]. In this approach, a variable is assigned as root or root node, and each node is then divided into sub-node according to the question about the interval of that variable which is either \"Yes\" or \"No\" which in turn indicates an input parameter that includes a prediction of output parameter in itself. Each branch in the DT shows the interval of the node which it is diverged from. The DT is usually drawn from top to bottom so that the roots are located at the top. A leaf is composed of roots, branches, and the final node. The DT includes various algorithms among which CHAID (chi-square automatic interaction detection), QUEST (quick, unbiased and efficient statistical tree), and CART are the most important [90; 91]. Reviewing the previous studies indicated  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ARIMA (p-q-d)** & **R-Squared** & **RMSE** & **MAPE** & **MAE** & **BIC** \\ \hline  & 0.9880 & 5.4392 & 4.1931 & 2.3836 & 3.4464 \\ ARIMA (2-1-2) & 0.9881 & 5.4361 & 4.4038 & 2.4034 & 3.4847 \\ ARIMA (0-1-2) & 0.988 & 5.431 & 4.195 & 2.391 & 3.443 \\ ARIMA (0-1-0) & 0.987 & 5.542 & 4.339 & 2.448 & 3.444 \\ ARIMA (1-1-0) & 0.988 & 5.469 & 3.997 & 2.362 & 3.438 \\ ARIMA (0-0-2) & 0.879 & 17.251 & 51.553 & 12.825 & 5.755 \\ ARIMA (0-0-1) & 0.713 & 26.589 & 83.031 & 20.340 & 6.600 \\ ARIMA (2-0-0) & 0.985 & 6.081 & 4.635 & 2.439 & 3.669 \\ ARIMA (1-0-1) & 0.985 & 6.052 & 4.642 & 2.441 & 3.660 \\ ARIMA (1-0-0) & 0.984 & 6.222 & 4.516 & 2.464 & 3.696 \\ ARIMA (0-1-1) & 0.988 & 5.447 & 3.986 & 2.350 & 3.429 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical results of different autoregressive integrated moving average (ARIMA) parameters for iron ore price forecasting.  
Figure 3: Residual plots of (ACF) and (PACF) by using ARIMA (0-1-1).  
that the CART model is more efficient and practical in the field of predicting and simulating compared to the other available ones. Therefore, this algorithm is selected and applied in the present study.  
The CART model was developed by [PERSON] et al. (2012) which can be made into a two-scale tree on the basis of some rules. This algorithm gives the capability to be used in parameters concerning quality and quantity. If the dependent parameter is of quantity type, the formed tree is called the \"Regression tree,\" and if it is of the quality type, it is named \"Classification tree.\" Parameters such as the \"Maximum tree depth\" and \"Number of intervals\" as controlling parameters are taken into consideration in this algorithm to avoid extreme complications of the model ([PERSON] et al., 2012). The MATLAB software was used to build the CART model. Many CART models considering the most effective parameters on this model, have been constructed and the best model among them was selected to predict price of iron ore. Figure 4 shows the desirable tree for modelling the iron ore price. In addition, Figure 5 displays the predicted iron ore price by CART verses their measured values. Based on this figure, R\({}^{2}\) is determined as 0.936 which revealed that the CART predictive model is able to estimate the iron ore price with high level of accuracy.  
Figure 4: Regression trees developed for iron ore price.