Aluminum Price Forecasting

Methodology

This project employed rigorous time series analysis techniques to develop accurate forecasting models for aluminum prices. The analysis began with exploratory data visualization and stationarity testing, followed by the implementation of three different types of models.

Data Preparation

The project utilized monthly price data for various metals, with the primary focus on aluminum. The dataset was split into a training set (up to 2010) and a test set (after 2010) to evaluate forecasting performance.

Stationarity Analysis

Augmented Dickey-Fuller (ADF) tests were conducted on differenced price series to confirm stationarity, a prerequisite for time series modeling. All differenced series showed strong evidence of stationarity with test statistics far below critical values.

Models Developed

Three different models were developed and compared to forecast aluminum prices:

Error Correction Model (ECM)

The ECM exploits the long-term equilibrium relationship between aluminum and copper prices. The model indicates that when aluminum prices deviate from their long-term relationship with copper, there is a tendency for them to return to equilibrium, albeit slowly.

Vector Autoregression (VAR)

The VAR model captures the dynamic relationships between changes in aluminum and copper prices, with optimal lag selection determined using information criteria. Analysis suggested the use of 11 lags for optimal modeling.

ARIMA with External Regressor

An ARIMA(0,1,1)(0,0,1)[12] model was fitted with copper prices as an external regressor, combining both seasonal and non-seasonal components in the autoregressive integrated moving average framework.

Results & Model Comparison

Models were evaluated using both information criteria (AIC/BIC) and forecast accuracy metrics (RMSE, MAPE, MAE) on the test set.

While the VAR model showed superior performance in terms of information criteria (AIC/BIC), the ARIMA model demonstrated the best out-of-sample forecast accuracy with the lowest error metrics.

Conclusion & Key Insights

Despite the VAR model having superior information criteria scores, the ARIMA model with copper as an external regressor demonstrated the best forecasting performance, indicating the importance of considering multiple evaluation metrics in time series modeling.

Key Findings

• Strong evidence of long-term relationships between aluminum and copper prices
• Differencing successfully achieved stationarity in all metal price series
• The ARIMA model provided the most accurate predictions despite not having the best information criteria scores
• The ECM model offered moderate performance with interpretable results about long-term relationships
• The VAR model, despite having the best AIC/BIC scores, did not translate to superior forecasting ability

Market Implications

The analysis suggests that copper prices are a valuable predictor of aluminum price movements, which has implications for traders, manufacturers, and other stakeholders in the metals industry. The forecasts predict continued upward trends in aluminum prices, with more stable growth than the volatile patterns observed in historical data.

Technical Implementation

This project was implemented in R using a range of specialized time series packages:

• readxl: For data import
• vars: For Vector Autoregression modeling
• mFilter: For time series filtering
• fpp3: For forecasting procedures
• broom: For model diagnostics
• forecast: For forecasting functions
• Metrics: For forecast accuracy evaluation

The analysis was conducted in a reproducible R markdown document (.qmd) which ensures transparency and reproducibility of all results.