ARIMA Time Series Modeling with the Addition of Intervention and Outlier Factors on Inflation Rate in Indonesia
DOI:
https://doi.org/10.31764/jtam.v8i1.17487Keywords:
ARIMA, Inflation, Economy, Forecasting, Accuracy.Abstract
Extreme events in a time series model can be detected when the precise timing of the event, known as the intervention, is known. When the exact timing of an event is unknown, it is referred to as an outlier. If these factors are neglected, the model's accuracy will be affected. To overcome this situation, it is possible to add the intervention or outlier factor into the time series model. This study proposes the combination of intervention and outlier analysis in time series models, especially ARIMA. It is intended to minimize the residuals and increase the accuracy of the model so that it is suitable for forecasting. Using the data of inflation rate in Indonesia, the conflict between Russia and Ukraine was used as an intervention factor in this case. Pre-intervention data (before February 2022) is used to construct the ARIMA model (1st model). After that, the modeling process continued by adding the intervention factor to the ARIMA model. The effect caused by the intervention allows an outlier to appear, so the process is continued by adding the outlier factor, called an additive outlier, into the model before (2nd model). The MAPE for the first and second models is 7.96% and 7.57%, respectively. The finding of this research shows that the ARIMA model with intervention and outlier factors, named as the 2nd model, is the best model. This study shows that combining the intervention and outlier factors into ARIMA model can improve the accuracy. The forecasting of the inflation rate in Indonesia for one period ahead in 2023 is in the range of 2.06%.
References
Alghamdi, T., Elgazzar, K., Bayoumi, M., Sharaf, T., & Shah, S. (2019). Forecasting Traffic Congestion Using ARIMA Modeling. 2019 15th International Wireless Communications & Mobile Computing Conference (IWCMC), 1227–1232. https://doi.org/10.1109/IWCMC.2019.8766698
Apostol, E.-S., Truică, C.-O., Pop, F., & Esposito, C. (2021). Change Point Enhanced Anomaly Detection for IoT Time Series Data. Water, 13(12), 1633. https://doi.org/10.3390/w13121633
Awe, O., Okeyinka, A., & Fatokun, J. O. (2020). An Alternative Algorithm for ARIMA Model Selection. 2020 International Conference in Mathematics, Computer Engineering and Computer Science (ICMCECS), 1–4. https://doi.org/10.1109/ICMCECS47690.2020.246979
Balbaa, M., Balbaa, M. E., Eshov, M., & Ismailova, N. (2022). The Impacts of Russian-Ukrainian War on the Global Economy. https://doi.org/10.13140/RG.2.2.14965.24807
Buckley, J., Fountain, J., Meuse, S., Whelan, C., Maguire, H., Harper, J. M., & Luiselli, J. K. (2020). Performance Improvement of Care Providers in a Child Services Setting: Effects of an Incentive-Based Negative Reinforcement Intervention on Data Recording. Child & Family Behavior Therapy, 42(2), 125–133. https://doi.org/10.1080/07317107.2020.1738733
Damian Adubisi, O., Jolayemi, E., & Adubisi, O. (2015). Estimating the Impact on the Nigeria Crude Oil Export from 2002 to 2013. (An Arima-Intervention Analysis). International Journal of Scientific & Engineering Research, 6(10), 878–886. http://www.ijser.org
Dewi, D. M., Ferrandy, A., Nafi, M. Z., & Nasrudin, N. (2023). The Impact of Covid-19 on Gold Price in Indonesia Using ARIMA Intervention. Journal of Business and Political Economy : Biannual Review of The Indonesian Economy, 2(2), 113–130. https://doi.org/10.46851/68
Elseidi, M. (2023). A hybrid Facebook Prophet-ARIMA framework for forecasting high-frequency temperature data. Modeling Earth Systems and Environment. https://doi.org/10.1007/s40808-023-01874-4
Guimarães, A. G., & da Silva, A. R. (2019). Impact of regulations to control alcohol consumption by drivers: An assessment of reduction in fatal traffic accident numbers in the Federal District, Brazil. Accident Analysis & Prevention, 127, 110–117. https://doi.org/10.1016/j.aap.2019.01.017
Hasan, E. A. (2019). A Method for Detection of Outliers in Time Series Data. International Journal of Chemistry, Mathematics and Physics, 3(3), 56–66. https://doi.org/10.22161/ijcmp.3.3.2
Hossein, S. (2021). Financial Sanctions and Economic Growth: An Intervention Time-series Approach. International Economics Studies, 51(1), 1–14. https://doi.org/10.22108/IES.2020.122915.1083
Huda, N. M., Mukhaiyar, U., & Imro’ah, N. (2022). An Iterative Procedure For Outlier Detection In Gstar(1;1) MODEL. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(3), 975–984. https://doi.org/10.30598/barekengvol16iss3pp975-984
Huda, N. M., Mukhaiyar, U., & Pasaribu, U. S. (2020). Forecasting dengue fever cases using autoregressive distributed lag model with outlier factor. AIP Conference Proceedings, 2268. https://doi.org/10.1063/5.0018450
Ilmiah, R. D., & Oktora, S. I. (2021). ARIMA Intervention Model for Measuring the Impact of the Lobster Seeds Fishing and Export Ban Policy on the Indonesian Lobster Export. Journal of Physics: Conference Series, 2123(1), 012011. https://doi.org/10.1088/1742-6596/2123/1/012011
Islam, Md. A. (2013). Impact of Inflation on Import: An Empirical Study. International Journal of Economics, Finance and Management Sciences, 1(6), 299. https://doi.org/10.11648/j.ijefm.20130106.16
Junaedi, J. (2022). The Impact of the Russia-Ukraine War on the Indonesian Economy. Journal of Social Commerce, 2(2), 71–81. https://doi.org/10.56209/jommerce.v2i2.29
Laome, L., Adhi Wibawa, G. N., Raya, R., Makkulau, & Asbahuna, A. R. (2021). Forecasting time series data containing outliers with the ARIMA additive outlier method. Journal of Physics: Conference Series, 1899(1), 012106. https://doi.org/10.1088/1742-6596/1899/1/012106
Lopez Bernal, J., Soumerai, S., & Gasparrini, A. (2018). A methodological framework for model selection in interrupted time series studies. Journal of Clinical Epidemiology, 103, 82–91. https://doi.org/10.1016/j.jclinepi.2018.05.026
Lukman Nugraha, A., Janwari, Y., Anton Athoillah, M., Mulyawan, S., & Islam Negri Sunan Gunung Djati, U. (2023). Inflation And Monetary Policy: Bank Indonesia’s Role in Suppressing the Inflation Rate of Islamic Economic Objectives. Islamic Economics and Business Review, 2(1), 70–82. https://ejournal.upnvj.ac.id/iesbir/article/view/5697
Mahia, F., Dey, A. R., Masud, M. A., & Mahmud, M. S. (2019). Forecasting Electricity Consumption using ARIMA Model. 2019 International Conference on Sustainable Technologies for Industry 4.0 (STI), 1–6. https://doi.org/10.1109/STI47673.2019.9068076
Mahkya, D. Al, & Anggraini, D. (2020). Forecasting the Number of Passengers from Bakauheni Port during the Sunda Strait Tsunami Period Using Intervention Analysis Approach and Outlier Detection. IOP Conference Series: Earth and Environmental Science, 537(1), 012009. https://doi.org/10.1088/1755-1315/537/1/012009
Maqsood, A., Burney, S. M. A., Safdar, S., & Jilani, T. (2019). OUTLIER DETECTION IN LINEAR TIME SERIES REGRESSION MODELS. Advances and Applications in Statistics. https://doi.org/10.13140/RG.2.2.12962.89289
Moghimi, B., Kamga, C., Safikhani, A., Mudigonda, S., & Vicuna, P. (2023). Non-Stationary Time Series Model for Station-Based Subway Ridership During COVID-19 Pandemic: Case Study of New York City. Transportation Research Record: Journal of the Transportation Research Board, 2677(4), 463–477. https://doi.org/10.1177/03611981221084698
Mohamad Ikhwan Syahtaria. (2022). Strategic review of the impact of the Russia-Ukraine war on Indonesian national economy. Global Journal of Engineering and Technology Advances, 12(3), 001–008. https://doi.org/10.30574/gjeta.2022.12.3.0148
Mohamed, J. (2020). Time Series Modeling and Forecasting of Somaliland Consumer Price Index: A Comparison of ARIMA and Regression with ARIMA Errors. American Journal of Theoretical and Applied Statistics, 9(4), 143. https://doi.org/10.11648/j.ajtas.20200904.18
Mukhaiyar, U., Huda, N. M., Novita Sari, R. K., & Pasaribu, U. S. (2019). Modeling Dengue Fever Cases by Using GSTAR(1;1) Model with Outlier Factor. Journal of Physics: Conference Series, 1366(1), 012122. https://doi.org/10.1088/1742-6596/1366/1/012122
Mukhaiyar, U., Yudistira, D., Indratno, S. W., & Yaacob, W. F. W. (2021). The Modelling of Heteroscedastics IDR-USD Exchange Rate with Intervention and Outlier Factors. Journal of Physics: Conference Series, 2084(1), 012002. https://doi.org/10.1088/1742-6596/2084/1/012002
Nasution, A. S., & Wulansari, I. Y. (2019). Analyzing Impacts of Renewable Energy Directive (RED) on Crude Palm Oil (CPO) Export and Forecasting CPO Export from Indonesia to European Union (EU) for 2019-2020 Using ARIMA Intervention Analysis. Proceedings of the International Conference on Trade 2019 (ICOT 2019). https://doi.org/10.2991/icot-19.2019.28
Schaffer, A. L., Dobbins, T. A., & Pearson, S. A. (2021). Interrupted time series analysis using autoregressive integrated moving average (ARIMA) models: a guide for evaluating large-scale health interventions. BMC Medical Research Methodology, 21(1). https://doi.org/10.1186/s12874-021-01235-8
Vadrevu, K. P., Eaturu, A., Biswas, S., Lasko, K., Sahu, S., Garg, J. K., & Justice, C. (2020). Spatial and temporal variations of air pollution over 41 cities of India during the COVID-19 lockdown period. Scientific Reports, 10(1). https://doi.org/10.1038/s41598-020-72271-5
Yu, C. (2023). The Change in Inflation Expectation During and Post the Pandemic in European Region. Highlights in Business, Economics and Management, 11, 236–240. https://doi.org/10.54097/hbem.v11i.8104
Zhou, Q., Hu, J., Hu, W., Li, H., & Lin, G. (2023). Interrupted time series analysis using the ARIMA model of the impact of COVID-19 on the incidence rate of notifiable communicable diseases in China. BMC Infectious Diseases, 23(1), 375. https://doi.org/10.1186/s12879-023-08229-5
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