Forecasting Indonesia’s Export Revenue through a Vector Autoregressive Exogenous Approach

Sudarwanto Sudarwanto; Syafa Marisha Puteri; Vera Maya Santi; Muhammad Arib Alwansyah

doi:10.31764/jtam.v10i2.36760

Forecasting Indonesia’s Export Revenue through a Vector Autoregressive Exogenous Approach

Sudarwanto Sudarwanto, Syafa Marisha Puteri, Vera Maya Santi, Muhammad Arib Alwansyah

Abstract

The Vector Autoregressive with Exogenous Variables (VARX) model extends the conventional VAR framework by explicitly incorporating external macroeconomic drivers, offering a more structurally informed approach to export forecasting. This study contributes to the literature by introducing a disaggregated modeling strategy that treats oil and gas exports and non-oil and gas exports as separate endogenous components, an aspect that has been largely overlooked in previous studies on Indonesia’s export performance. By positioning VARX as a system-based forecasting tool rather than a purely statistical extension, this research provides an updated methodological perspective on export revenue analysis. Using monthly data from January 2015 to December 2024, this study evaluates several VARX specifications that integrate the rupiah–US dollar exchange rate and West Texas Intermediate (WTI) crude oil prices as exogenous variables. Model selection is conducted based on a combination of information criteria and forecasting performance indicators, leading to the identification of VARX(5,6) as the most suitable specification. The inclusion of exogenous variables is shown to substantially enhance predictive accuracy, confirming the relevance of external economic shocks in shaping Indonesia’s export revenue dynamics. Empirical results indicate that WTI oil prices exert a significant causal influence on export revenue, while the exchange rate effect becomes meaningful when jointly evaluated with oil prices and endogenous export components. The selected VARX(5,6) model demonstrates strong forecasting performance, achieving a MAPE of 5.60% and an nRMSE of 6.40%. From a policy standpoint, these findings suggest that export planning and stabilization policies should explicitly account for global oil price volatility and exchange rate interactions. The proposed VARX framework can therefore serve as a practical analytical tool for policymakers to anticipate short-term export fluctuations and design responsive trade and macroeconomic strategies under external uncertainty.

Keywords

Exchange Rate; Export; Forecasting; Modeling; VARX.

Full Text:

DOWNLOAD [PDF]

References

Akal, M. (2015). A VARX modelling of energy intensity interactions between China, the United States, Japan and EU. OPEC Energy Review March 2015, 103-124. https://doi.org/10.1111/opec.12044.

Akanbi, O. B., & Bello, A. O. (2024). Fitting Autoregressive Integrated Moving Average with Exogenous Variables Model with Lognormal Error Term. Journal of Scientific Research and Reports, 30(10), 158–168. https://doi.org/10.9734/jsrr/2024/v30i102442.

Alnashwan, O. S. (2017). Using VARX Model to Forecast the Effect of Culvation of Main Crops on Water Security in Saudia Arabia. Journal of Experimental Biology and Agricurtural Sciences, 5(Spl-1-SAFSAW), 127-135. http://dx.doi.org/10.18006/2017.5(Spl-1-SAFSAW).S126.S135.

Armstrong, J. S. (2007). Significance Tests Harm Progress in Forecasting. International Journal of Forecasting, 23(2), 321-327. https://doi.org/10.1016/j.ijforecast.2007.03.004

Belomestny, D., Krymova, E., & Polbin, A. (2021). Bayesian TVP-VARX models with time invariant long-run multipliers. Economic Modelling, 101(May), 105531. https://doi.org/10.1016/j.econmod.2021.105531.

Box, G. E. (2016). Time Series Analysis Forecasting and Control (5th ed.). Hoboken, New Jersey, United States of America: John Wiley & Sons. https://doi.org/10.1111/jtsa.12194

Brockwell, P. J. (2016). Introduction to Time Series and Forecasting edition 3rd. Cham, Swiss: Springer International Publishing Switzerland. https://link.springer.com/book/10.1007/978-3-319-29854-2

Ee, C. Y. (2016). Export-Led Growth Hypothesis: Empirical Evidence from Selected Sub-Saharan African Countries. Prosidea Economics & Finance, 35, 232-240. https://doi.org/10.1016/S2212-5671(16)00029-0.

Eshete, Z. S. (2018). Modeling the Dynamics of Sectoral TFP Growth in Ethiopia: Explaining Persistent Economic Debacles. Journal of Sustainable Development Studies, 11(2), 120-174. http://www.openscienceonline.com/journal/archive2?journalId=709&paperId=992.

Filippidis, M., Filis, G., Magkonis, G., & Tzouvanas, P. (2023). Evaluating robust determinants of the WTI/Brent oil price differential: A dynamic model averaging analysis. Journal of Futures Markets, 43(6), 807–825. https://doi.org/10.1002/fut.22414.

Haydier, E. A., Albarwari, N. H., & Ali, T. H. (2023). The Comparison Between VAR and ARIMAX Time Series Models in Forecasting. Iraqi Journal of Statistical Sciences, 20(2), 249-262. http://dx.doi.org/10.33899/iqjoss.2023.181260.

Jadhav, V. a. (2017). Application of ARIMA Model for Forecasting Agricultural Prices. Journal Agricultural Science and Technology (JAST), 19(5) 981-992. https://dor.isc.ac/dor/20.1001.1.16807073.2017.19.5.7.0.

Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. New York, United States of America: Springer-Verlag Berlin Heidelberg. doi: 10.1007/978-3-540-27752-1

Ministry of Trade of the Republic of Indonesia. (2025, January 10). Indonesian Trade Balance. One Trade Data: https://satudata.kemendag.go.id/data-informasi/perdagangan-luar-negeri/neraca-perdagangan-indonesia.

Nicholson, W. B. (2017). VARX-L: Structured regularization for large vector autoregressions with exogenous variables. International Journal of Forecasting, 33(3) 627-651. https://doi.org/10.1016/j.ijforecast.2017.01.003.

Paul, R. K. (2015). ARIMAX-GARCH-WAVELET model for forecasting volatile data. Model Assisted Statistics and Applications, 10(3), 243–252. https://doi.org/10.3233/MAS-150328.

Peter, D. a. (2012). ARIMA vs. ARIMAX – which approach is better to analyze and forecast macroeconomic time series, (2). Proceedings of 30th international conference mathematical methods in economics, 136-140.

https://www.researchgate.net/publication/394547336_ARIMA_vs_ARIMAX-which_approach_is_better_to_analyze_and_forecast_macroeconomic_time_series

Santi, V. M. (2023). Forecasting the Value of Indonesia's Oil and Gas Imports Using Seasonal Autoregressive Integrated Moving Average. BAREKENG: Journal of Mathematics and Its Applications, 17(4), 2047–2058. https://doi.org/10.30598/barekengvol17iss4pp2047-2058.

Setiawan, S., Sohibien, G. P. D., Prastyo, D. D., Akbar, M. S., & Kamil, A. A. (2024). Addition of Subset and Dummy Variables in the Threshold Spatial Vector Autoregressive with Exogenous Variables Model to Forecast Inflation and Money Outflow. Economies, 12(12), 1 - 27. https://doi.org/10.3390/economies12120352.

Shcherbakov, M. V. (2013). A Survey of Forecast Error Measures. World Applied Sciences Journal, 24(24),i 171-176. http://dx.doi.org/10.5829/idosi.wasj.2013.24.itmies.80032.

Slatina, E., Lazović-Pita, L., Abdić, A., & Abdić, A. (2023). The Relationship Between Oil Prices and Stock Prices of the European Renewable Energy Companies: A Vector Autoregressive Analysis. Naše Gospodarstvo/Our Economy, 69(4), 1–11. https://doi.org/10.2478/ngoe-2023-0019.

Sukono and Ibrahim, R. A. (2023). Forecasting the Effectiveness of COVID-19 Vaccination Using Vector Autoregressive with an Exogenous Variable: On the Cases of COVID-19 in Indonesia. Hindiawi. https://doi.org/10.1155/2023/6285328.

Sutthichaimethee, P. a. (2020). A Forecasting Model on Carrying Capacity for Government’s Controlling Measure under Environmental Law in Thailand: Adapting Non-recursive Autoregression Based on the Var-X Model. International Journal of Energy Economics and Policy, 10(6), 645-655. http://dx.doi.org/10.32479/ijeep.9439.

Tsay, R. S. (2005). Analysis of Financial Time Series (2nd ed.). Hoboken, New Jersey, United States of America: John Wiley & Sons, Inc. doi:10.1002/0471746193

Wei, W. W. (2006). Time Series Analysis Univariate and Multivariate Methods (2nd ed.). Philadelphia, Pennsylvania: Pearson. https://civil.colorado.edu/~balajir/CVEN6833/lectures/wwts-book.pdf

Woodward, W. A. (2022). Time Series for Data Science Analysis and Forecasting (1st ed.). Boca Raton, United States of America: CRC Press. https://doi.org/10.1201/9781003089070

Xu, Q. (2024). Quantifying the Impact of the COVID-19 Pandemic on Copper Price Trends Using Time Series Analysis. Highlights in Science, Engineering and Technology, 88, 1251–1256. https://doi.org/10.54097/j5t0eg31.

Yulianti, S. R., & Effendie, A. R. (2024). Improving the Accuracy of Discrepancies in Farmers. JTAM (Jurnal Teori dan Aplikasi Matematika), 8(3), 994 - 1011. https://doi.org/10.31764/jtam.v8i3.22584.

DOI: https://doi.org/10.31764/jtam.v10i2.36760