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

Umi Mahmudah*    -  Universitas Islam Negeri K.H. Abdurrahman Wahid Pekalongan, Indonesia

(*) Corresponding Author
DOI: 10.21580/jnsmr.v10i1.18887

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.

Keywords: autoregressive; bootstrap; forecasting; oil and gas

  1. Alqahtani, A., & Klein, T. (2021). Oil price changes, uncertainty, and geopolitical risks: On the resilience of GCC countries to global tensions. Energy, 236, 121541. https://doi.org/https://doi.org/10.1016/j.energy.2021.121541
  2. Chai, J., Zhang, X., Lu, Q., Zhang, X., & Wang, Y. (2021). Research on imbalance between supply and demand in China’s natural gas market under the double-track price system. Energy Policy, 155, 112380. https://doi.org/https://doi.org/10.1016/j.enpol.2021.112380
  3. Chamdani, M., Mahmudah, U., & Fatimah, S. (2019). Prediction of Illiteracy Rates in Indonesia Using Time Series. International Journal of Education, 12(1), 34–41. https://doi.org/10.17509/ije.v12i1.16589
  4. Chernick, M. R. M. R., & LaBudde, R. A. R. A. R. A. (2014). An introduction to bootstrap methods with applications to R. John Wiley & Sons.
  5. Clements, M. P., & Kim, J. H. (2007). Bootstrap prediction intervals for autoregressive time series. Computational Statistics & Data Analysis, 51(7), 3580–3594.
  6. Cunado, J., Gupta, R., Lau, C. K. M., & Sheng, X. (2020). Time-varying impact of geopolitical risks on oil prices. Defence and Peace Economics, 31(6), 692–706. https://doi.org/https://doi.org/10.1080/10242694.2018.1563854
  7. De Livera, A. M., Hyndman, R. J., & Snyder, R. D. (2011). Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American Statistical Association, 106(496), 1513–1527. https://doi.org/https://doi.org/10.1198/jasa.2011.tm09771
  8. Demirbas, A., Omar Al-Sasi, B., & Nizami, A.-S. (2017). Recent volatility in the price of crude oil. Energy Sources, Part B: Economics, Planning, and Policy, 12(5), 408–414. https://doi.org/https://doi.org/10.1080/15567249.2016.1153751
  9. El-Gamal, M. A., & Jaffe, A. M. (2018). The coupled cycles of geopolitics and oil prices. Economics of Energy & Environmental Policy, 7(2), 1–14. https://doi.org/https://www.jstor.org/stable/27030624
  10. Errouissi, R., Cardenas-Barrera, J., Meng, J., Castillo-Guerra, E., Gong, X., & Chang, L. (2015). Bootstrap prediction interval estimation for wind speed forecasting. 2015 IEEE Energy Conversion Congress and Exposition (ECCE), 1919–1924.
  11. Hyndman, R. J. R. J., & Athanasopoulos, G. (2018). Forecasting: principles and practice. OTexts. https://otexts.com/fpp3/
  12. Kilian, L. (1998). Confidence intervals for impulse responses under departures from normality. Econometric Reviews, 17(1), 1–29. https://doi.org/https://doi.org/10.1080/07474939808800401
  13. Kim, J. H. (2001). Bootstrap-after-bootstrap prediction intervals for autoregressive models. Journal of Business and Economic Statistics, 19(1), 117–128. https://doi.org/10.1198/07350010152472670
  14. Kim, J. H., & Shamsuddin, A. (2020). A bootstrap test for predictability of asset returns. Finance Research Letters, 35, 101289.
  15. Mahmudah, U. (2023). Robust Prediction Intervals for Indonesian Inflation: A Bias-Corrected Bootstrap Approach. Journal of Fundamental Mathematics and Applications (JFMA), 6(2). https://doi.org/https://doi.org/10.14710/ihis.v%vi%i.20502
  16. Mahmudah, U., Surono, S., Wahyu Prasetyo, P., & E Haryati, A. (2023). Forecasting educated unemployed people in Indonesia using the Bootstrap Technique. Journal of Mahani Mathematical Research, 12(1), 171–182. https://doi.org/10.22103/JMMR.2022.19368.1239
  17. Masarotto, G. (1990). Bootstrap prediction intervals for autoregressions. International Journal of Forecasting, 6(2), 229–239.
  18. Noguera-Santaella, J. (2016). Geopolitics and the oil price. Economic Modelling, 52, 301–309. https://doi.org/https://doi.org/10.1016/j.econmod.2015.08.018
  19. Razmi, F., Azali, M., Chin, L., & Habibullah, M. S. (2016). The role of monetary transmission channels in transmitting oil price shocks to prices in ASEAN-4 countries during pre-and post-global financial crisis. Energy, 101, 581–591. https://doi.org/https://doi.org/10.1016/j.energy.2016.02.036
  20. Staszewska-Bystrova, A., Staszewska‐Bystrova, A., & Staszewska-Bystrova, A. (2011). Bootstrap prediction bands for forecast paths from vector autoregressive models. Journal of Forecasting, 30(8), 721–735. https://doi.org/10.1002/for.1205
  21. Su, C.-W., Qin, M., Tao, R., Moldovan, N.-C., & Lobonţ, O.-R. (2020). Factors driving oil price——from the perspective of United States. Energy, 197, 117219. https://doi.org/https://doi.org/10.1016/j.energy.2020.117219
  22. Thombs, L. A., & Schucany, W. R. (1990). Bootstrap prediction intervals for autoregression. Journal of the American Statistical Association, 85(410), 486–492.

Open Access Copyright (c) 2024 Journal of Natural Sciences and Mathematics Research
Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Journal of Natural Sciences and Mathematics Research
Published by Faculty of Science and Technology
Universitas Islam Negeri Walisongo Semarang

Jl Prof. Dr. Hamka Kampus III Ngaliyan Semarang 50185
Website: https://journal.walisongo.ac.id/index.php/JNSMR
Email:jnsmr@walisongo.ac.id

ISSN: 2614-6487 (Print)
ISSN: 2460-4453 (Online)

View My Stats

Lisensi Creative Commons

This work is licensed under a Creative Commons Lisensi Creative Commons .

apps