Time Series Analysis Using AR Methods for Oil Price Forecasting

In this article, we will conduct an in-depth analysis and forecasting of oil prices using Autoregressive (AR) models from time series analysis. The implementation begins with employing the Bayesian Information Criterion (BIC) to determine the optimal order of the AR model, which involves comparing different lag structures and selecting the model with the lowest BIC value to balance goodness-of-fit and model complexity. Subsequently, we will estimate the parameters of the AR model using the least squares method, where the algorithm minimizes the sum of squared residuals between actual oil prices and model predictions. This can be implemented through matrix operations solving the normal equations or using optimization techniques in programming environments like Python's statsmodels or MATLAB's arima function. We will also examine the residuals from the AR model, conducting diagnostic checks including tests for white noise properties using autocorrelation function (ACF) plots and Ljung-Box tests to validate model adequacy. Model improvement strategies will be discussed, such as addressing residual autocorrelation through model refinement or considering alternative ARMA/ARIMA specifications. Finally, we will utilize the fitted AR model to generate oil price forecasts, implementing prediction intervals to assess forecast uncertainty. The reliability and accuracy of predictions will be evaluated using metrics like Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), with backtesting procedures to validate model performance on historical data. Through this comprehensive analysis, we will gain deeper insights into oil price fluctuation patterns and trends, providing valuable references and foundations for future investment decisions and strategic planning.