Bootstrap-after-bootstrap for autoregressive models: an application to Indonesian value of export oil and gas

This research focuses on predicting the value of oil and gas exports in Indonesia, employing a hybrid methodology that combines autoregressive models and a bootstrap approach. Specifically, this research applies the bootstrap-after-bootstrap approach to showcase its effectiveness in improving the accuracy of parameter estimates. Analysis results indicate that the autoregressive model with an order of p=2 minimizes the AIC, BIC, and HQ values, yielding AIC=9.833775, BIC=10.03125, and HQ=9.883440, respectively. Consequently, the AR(2) model emerges as the optimal choice for predicting Indonesia's export value of oil and gas. This research utilizes varying numbers of bootstrap replications (B=100, 250, 500, 1000, and 10000) to assess the impact on prediction intervals. Prediction intervals exhibit less smoothness for B=100 and B=250, whereas B=500 and B=1000 result in a considerably smoother pattern. The highest level of smoothness is achieved for B=10000. The findings underscore that bootstrap-after-bootstrap prediction intervals provide the most accurate and conservative assessment of future uncertainty. Moreover, predictive analysis for the upcoming five periods indicates a projected decline in the export value of oil and gas in Indonesia. Overall, this research demonstrates the efficacy of the bootstrap-after-bootstrap approach in enhancing the precision of predictions and providing robust insights into future uncertainties surrounding Indonesia's oil and gas export market.