THE PROMINENCE OF VECTOR AUTOREGRESSIVE MODEL IN MULTIVARIATE TIME SERIES FORECASTING MODELS WITH STATIONARY PROBLEMS
Abstract
One of the problems in modelling multivariate time series is stationary. Stationary test results do not always produce all stationary variables; mixed stationary and non-stationary variables are possible. When stationary problems are found in multivariate time series modelling, it is necessary to evaluate the model's performance in various stationary conditions to obtain the best forecasting model. This study aims to get a superior multivariate time series forecasting model based on the goodness of the model in various stationary conditions. In this study, the evaluation of the model's performance through simulation data modelling is then applied to the actual data with a stationary problem, namely Bogor City inflation data. The best model in simulation modelling is based on the stability of RMSE and MAD in 100 replications. The results are that the VAR model is the best in various stationary conditions. Meanwhile, the best model on actual data modelling is based on evaluation in 4 folds for model fitting power and model forecasting power. The Bogor City inflation data modelling with the mixed stationary problem resulted in the best model, namely the VAR(1) model. This means the VAR model is good enough to be used as a forecasting model in mixed stationary conditions. Thus, in this study, based on the goodness of the model in two modelling scenarios in various stationary conditions, overall, it was found that the VAR model was superior to the VARD and VECM models.
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References
W. Enders, Applied Econometric Time series, 4th ed. USA: J Wiley, 2014.
A. Salim and Fadilla, “Pengaruh Inflasi Terhadap Pertumbuhan Ekonomi Indonesia Anggun Purnamasari,” Ekon. Sharia J. Pemikir. dan Pengemb. Ekon. Syariah, vol. 7, no. 1, pp. 17–28, 2021, [Online]. Available: www.bps.go.id,.
E. Pranyoto, “Analisis Kointegrasi dan Kausalitas Engel Granger Tingkat Suku Bunga Simpanan , Perubahan Nilai Tukar Rp/USD dan return Pasar Saham Di Bursa Efek,” J. Bisinis Darmajaya, vol. 03, no. 02, 2017.
Iskandar, “Analisis Vector Autoregression (VAR) Terhadap Interrelationship Antara Financing Deposit Ratio (FDR) DAN Return ON Asset (ROA) Pada Bank Syariah Di Indonesia,” J. JESKape, vol. 3, no. 2, pp. 19–39, 2019.
Erwandi, F. M. Afendi, and B. Waryanto, “Analisis Pengaruh Daerah Pemasok Terhadap Harga Cabai Merah Di Dki Jakarta Menggunakan Vector Error Correction Model (Vecm),” Indones. J. Stat. Its Appl., vol. 3, no. 3, pp. 216–235, 2019, doi: 10.29244/ijsa.v3i3.276.
L. M. Hamzah, S. U. Nabilah, E. Russel, M. Usman, E. Virginia, and Wamiliana, “Dynamic Modelling and Forecasting of Data Export of Agricultural Commodity by Vector Autoregressive Model,” J. Southwest Jiatong Univ., vol. 55, no. 3, 2020.
S. Aktivani, “Uji Stationeritas Data Inflasi Kota Padang Periode 2014-2019,” J. Stat. Ind. dan Komputasi, vol. 6, no. 1, pp. 26–33, 2021.
M. R. Susila, “Pemodelan Multivariat Kunjungan Wisatawan Dan Darat Yang Melibatkan Dampak Wabah Covid-19,” vol. 15, no. 3, pp. 467–478, 2021.
R. H. Assaad and S. Fayek, “Predicting the Price of Crude Oil and its Fluctuations Using Computational Econometrics: Deep Learning, LSTM, and Convolutional Neural Networks,” Econom. Res. Financ., vol. 6, no. 2, pp. 119–137, 2021, doi: 10.2478/erfin-2021-0006.
P. A. V. B. Swamy and P. von zur Muehlen, “Cointegration: Its fatal flaw and a proposed solution,” Sustain. Futur., vol. 2, p. 100038, 2020, doi: 10.1016/j.sftr.2020.100038.
J. Van Greunen, A. Heymans, C. Van Heerden, and G. Van Vuuren, “The prominence of stationarity in time series forecasting,” J. Stud. Econ. Econom., vol. 38, no. 1, pp. 1–16, 2014, doi: 10.1080/10800379.2014.12097260.
F. Bashir and H. L. Wei, “Handling missing data in multivariate time series using a vector autoregressive model-imputation (VAR-IM) algorithm,” Neurocomputing, vol. 000, pp. 1–8, 2017, doi: 10.1016/j.neucom.2017.03.097.
E. Zivot and J. Wang, “Modelling Financial Time Series with S-PLUS,” J. R. Stat. Soc. Ser. A (Statistics Soc)., 2016, doi: 10.1111/j.1467-985x.2007.00506_20.x.
K. Bulteel, F. Tuerlinckx, A. Brose, and E. Ceulemans, “Clustering vector autoregressive models: Capturing qualitative differences in within-person dynamics,” Front. Psychol., vol. 7, no. OCT, pp. 1–15, 2016, doi: 10.3389/fpsyg.2016.01540.
A. Suharsono, A. Aziza, and W. Pramesti, “Comparison of vector autoregressive (VAR) and vector error correction models (VECM) for index of ASEAN stock price,” in AIP Conference Proceedings, 2017, vol. 1913, doi: 10.1063/1.5016666.
R. M. Ueda, A. M. Souza, and R. M. C. P. Menezes, “How macroeconomic variables affect admission and dismissal in the Brazilian electro-electronic sector: A VAR-based model and cluster analysis,” Phys. A Stat. Mech. its Appl., vol. 557, p. 124872, 2020, doi: 10.1016/j.physa.2020.124872.
E. G. Elizabeth, C. S. Nicole, K. S. Damian, and F. S. Anne, “Using Vector Autoregression Modeling to Reveal Bidirectional Relationships in Gender/Sex-Related Interactions in Mother–Infant Dyads,” Front. Psychol., vol. 11, no. August, pp. 1–19, 2020, doi: 10.3389/fpsyg.2020.01507.
T. Chai and R. R. Draxler, “Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature,” Geosci. Model Dev., vol. 7, no. 3, pp. 1247–1250, 2014, doi: 10.5194/gmd-7-1247-2014.
U. Khair, H. Fahmi, S. Al Hakim, and R. Rahim, “Forecasting Error Calculation with Mean Absolute Deviation and Mean Absolute Percentage Error,” J. Phys. Conf. Ser., vol. 930, no. 1, 2017, doi: 10.1088/1742-6596/930/1/012002.
J. Yuan, Y. Xu, and X. Zhang, “Income Growth, Energy Consumption, and Carbon Emissions: The Case of China,” Emerg. Mark. Financ. Trade, vol. 50, no. 5, pp. 169–181, 2014, doi: 10.2753/REE1540-496X500512.
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