# Copper Price Prediction Using Support Vector Regression Technique
## 5 Methodology
### Step 4: Performance Measures
Using monthly data, the authors estimated linear and threshold autoregressive models. For the nonlinear models, they assumed that the dynamics of metal prices depend on their deviation from the recursive mean. We use a monthly prediction (30 days) to compare the best RMSE value obtained in both works. Our RMSE (0.033) is similar to the RMSE (0.046) obtained in that work. * In [8], the authors use time series models to predict the prices of Shanghai copper futures. This work introduces the application of X12-ARIMA-GARCH family models in futures price analysis and forecasting. To compare their results with ours, we use a short prediction period (5 and 10 days) and compare the RMSE obtained. In the same period, our RMSE (0.017 and 0.018) are similar to the RMSE (0.018 and 0.022) in that work. * In [5], a hybrid model is proposed to provide an accurate model for predictions of copper prices. The proposed model combines the adaptive neuro-fuzzy inference system and genetic algorithm. Our work presents an RMSE (\(RMSE=0.033\)) similar to the GA-ANFIS method (\(RMSE=0.0813\)), presented in that work. This is due to the granularity of the training and prediction data. It is interesting to note that in that work, a method based on SVM is shown whose error (\(RMSE=0.1027\)) is high compared to our work. The difference is that in our work, a regression was used with an exhaustive search of its parameters. * In [20], a Bat algorithm was used to predict the copper price volatility. The copper price was estimated using time series and Bat algorithms. The time series function used in this work is similar in our work. Under those conditions, the prediction error is \(RMSE=0.132\). With the method proposed in this work, a maximum error of \(RMSE=0.08\) is achieved (see Table 2). Figure 4: MSE. (**a**) Distribution of MSE for type and interval. (**b**) 95% family-wise confidence level. Finally, we can observe in Figure 4a that there are significant differences of the MSE at 95% confidence, between \(S_{a}\to S_{b}\) and \(S_{b}\to S_{a}\) in each of the prediction intervals 5, 10, 15, 20, 25 and 30 days. In contrast, for the prediction \(S_{a}\to S_{b}\), there are no significant differences in the MSE between the prediction intervals 5, 10, 15, 20, 25 and 30 days. This allows us to show the robustness of the prediction in the short and medium-term since the prediction at the five-day interval has not lost performance over the 30-day prediction interval, considering it, in this case, as a medium-term. This is useful for the decision-making process for mining companies and traders. On the other hand, to affect the decision-making process for investors and the government, it is necessary to have reliable long-term forecasts. ## 8 Conclusions

In this work, the construction of a model was presented based on SVR that allows making a prediction of the closing value of copper in the Metal London Stock Exchange, as the RMSE was equal to or less than the 2.2% for prediction periods of 5 and 10 days. The method consists of finding the best model through a search in a grid, wherein each model is trained and tested through use of the balancing methods in cross-validation. For the training process, only the data of closing price of the series are used. The results indicate that the model of the SVR can be used regardless of the number of days of the prediction, and this can be done with only three actual values.Additionally, we observed that more current data negatively impact the MSE. This phenomenon must be studied in the future, but there is a signal that this can be explained through the level of noise and the amount of data of the training time series. The importance of price prediction will depend on the interest of the agents and their objectives in short, medium and long-term prediction periods. Our work aims for short-term predictions of 5 days, 10,..., up to 30 days. These predictions will interest brokers and investors who seek to take advantage of the periodic variations with active portfolio management.