Arıma ve gri tahmin modellerinde Fourier serisi modifikasyonu: Türkiye enflasyonu uygulaması

Year 2021, Volume: 14 Issue: 2, 559 - 577, 12.04.2021

Buğra Bağcı

https://doi.org/10.25287/ohuiibf.741258

Cited By: 1

Abstract

Günümüzde birçok merkez bankası enflasyonu kontrol altında tutarak fiyat istikrarını sağlayan istikrarlı bir ekonomik yapı kurmaya çalışmaktadır. Özellikle gelişmekte olan ülkeler diğer makroekonomik dengeleri de olumsuz etkilediği için yüksek enflasyon üzerine yoğunlaşmaktadırlar. Bu yönüyle fiyat istikrarının sürdürülmesi birçok ülkenin politika yapıcılarının ana hedefi haline gelmiştir. Özellikle enflasyon verilerinin tahmini, çok geniş kitleleri etkilemesi bakımından daha da önemli hale gelebilmektedir. Enflasyon verileri de, önemi göz önünde bulundurularak çalışmamızda kullanılmıştır. Bu anlamda tahmin etmek kadar, yapılan tahminin doğruluğunun da hayati olduğu düşünülmüştür. Bu çalışmada öncelikle, literatürde sıkça kullanılan iki farklı tahmin tekniği olan ARIMA modeli ve GM(1,1) modeli ile Türkiye’de enflasyon oranı tahmin edilerek hata terimleri hesaplanmıştır. Elde edilen bu hata terimleri, Fourier serileri yardımıyla modifiye edilerek yeni tahmin değerleri elde edilmiş ve doğruluk oranları arttırılmıştır. Orijinal modeller ile yapılan tahminlemelerde ARIMA modelinin GM(1,1) modelinden daha başarılı olduğu görülmüştür. Sonrasında, Fourier modifikasyonu uygulanmış ve bu modellerin modellerin orijinal modellerden çok daha başarılı sonuçlar ürettiği, en başarılı sonucun da Fourier modifikasyonlu GM(1,1) modeline ait olduğu görülmüştür. Gelecek dönem tahminlerinde de benzer durum söz konusu olmuştur. Türkiye açısından bakıldığında enflasyonun ciddi bir düşüş eğilimi göstermeyeceği ve bu konu üzerine yoğunlaşılması gerektiği söylenebilir.

Keywords

Tahmin modelleri, ARIMA Model, Gri Tahmin Modeli, Fourier Hata Düzeltmesi, Enflasyon Tahmini

Fourier series modification in Arima and grey prediction models: A case of Turkey's inflation

Abstract

Many central banks are trying to establish a stable economic structure that ensures price stability by keeping inflation under control. Especially developing countries concentrate on high inflation since it affects other macroeconomic balances negatively. In this respect, maintaining price stability has become the main goal of many countries' policy makers. In particular, the estimation of inflation data can become even more important as it affects a wide audience. Inflation data was also used in our study, considering its importance. In this sense, it is known that the accuracy of the prediction is as vital as the forecast. In this study, two different estimation techniques commonly used in the literature that ARIMA model and GM (1,1) model estimated the Turkey’s inflation rate and the error terms are calculated. These error terms were modified with the Fourier series and new prediction values were obtained and their accuracy rates were increased. It has been observed that the ARIMA model is more successful than the GM (1,1) model on the models installed with the original models. Then, it has been observed that the models with Fourier modification produced much more successful results than the original models, and the most successful result belonged to the Fourier modified GM(1,1) model. A similar situation occurred in the future projections. From the perspective of Turkey, where inflation will not showing a downward trend seriously and said that it should focus on this issue.

Keywords

Forecasting Models, ARIMA Model, Grey Prediction Model, Fourier Residual Modification, Forecasting Inflation

References

• Afshar, N. R., & Fahmi, H. (2012). Rainfall forecasting using Fourier series. Journal of Civil Engineering and Architecture, 6(9), 1258.
• Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.
• Chen, X., Jiang, K., Liu, Y., (2015). Inflation prediction for China based on the Grey Markov model? In 2015 IEEE International Conference on Grey Systems and Intelligent Services (GSIS) (pp. 301-306). IEEE.
• Deng, J.L. (1982). Control problems of grey systems. Sys. & Contr. Lett., 1(5), 288-294.
• Deng, J.L. (1989). Introduction to grey system theory. The Journal Of Grey System, 1(1), 1-24.
• Erilli, N.A., Eğrioğlu, E., Yolcu, U., Aladağ, Ç.H., Uslu, V.R., (2010). Türkiye’de enflasyonun ileri ve geri beslemeli yapay sinir ağlarının melez yaklaşımı ile öngörüsü. Doğuş Üniversitesi Dergisi, 11 (1), 42-55.
• Eze, C. M., Asogwa, O. C., Onwuamaeze, C. U., Eze, N. M., & Okonkwo, C. I. (2020). On the fourier residual modification of ARIMA models in modeling malaria ıncidence rates among pregnant women. American Journal of Theoretical and Applied Statistics, 9(1), 1-7.
• Garcia, M.G., Medeiros, M.C., Vasconcelos, G.F., (2017). Real-time inflation forecasting with high dimensional models: The case of Brazil. International Journal of Forecasting, 33(3), 679-693.
• Groen, J.J., Paap, R., Ravazzolo, F., (2013). Real-time inflation forecasting in a changing world. Journal of Business & Economic Statistics, 31(1), 29-44.
• Guo, Z., Song, X., Ye, J., (2005). A Verhulst model on time series error corrected for port throughput forecasting. Journal of the Eastern Asia society for Transportation studies, 6, 881-891.
• Hubrich, K., (2005). Forecasting euro area inflation: Does aggregating forecasts by HICP component improve forecast accuracy?. International Journal of Forecasting, 21(1), 119-136.
• Inoue, A., Kilian, L., (2008). How useful is bagging in forecasting economic time series? A case study of US consumer price inflation. Journal of the American Statistical Association, 103(482), 511-522.
• Iwok, I. A., & Udoh, G. M. (2016). A Comparative study between the ARIMA-Fourier Model and the Wavelet model. American Journal of Scientific and Industrial Research, 7(6), 137-144.
• Kayacan, E., Ulutas, B., Kaynak, O., (2010). Grey system theory-based models ın time series prediction. Expert Systems With Applications, 37(2), 1784-1789.
• Koop, G., Korobilis, D., (2012). Forecasting inflation using dynamic model averaging. International Economic Review, 53(3), 867-886.
• Liu, S.F., Yang, Y.J., Wu, L.F., and Xie, N.M. (2014). Grey System Theory and Its Application, Vol. 6.
• Luis, J., Hector, J., 2013. Forecasting Mexican inflation using neural networks. In CONIELECOMP 2013, 23rd International Conference on Electronics, Communications and Computing.
• Meçik, O., Karabacak, M., (2011). ARIMA modelleri ile enflasyon tahminlemesi: Türkiye uygulaması. Sosyal Ekonomik Araştırmalar Dergisi, 11(22), 177-198.
• Meyler, A., Kenny, G., Quinn, T., (1998). Forecasting Irish inflation using ARIMA models.
• Moshiri, S., Cameron, N., (2000). Neural network versus econometric models in forecasting inflation. Journal of Forecasting, 19(3), 201-217.
• Nakamura, E., (2005). Inflation forecasting using a neural network. Economics Letters, 86(3), 373-378.
• Nguyen, T. L., Chen, P. J., Shu, M. H., Hsu, B. M., & Lai, Y. C. (2013). Forecasting with Fourier residual modified ARIMA model: The case of air cargo in Taiwan. In Diversity, Technology, and Innovation for Operational Competitiveness: Proceedings of the 2013 International Conference on Technology Innovation and Industrial Management (pp. 5-135). To Know Press.
• Orhunbilge, N., (1999). Zaman Serileri Analizi Tahmin ve Fiyat Endeksleri, Avcıol Basım Yayın.
• Öğünç, F., Akdoğan, K., Başer, S., Chadwick, M.G., Ertuğ, D., Hülagü, T., ..., Tekatlı, N., (2013). Short-term inflation forecasting models for Turkey and a forecast combination analysis. Economic Modelling, 33, 312-325.
• Saremi, A., Pashaki, M.H.K., Sedghi, H., Rouzbahani, A., & Saremi, A. (2011). Simulation of river flow using Fourier series models. In International Conference on Environmental and Computer Science vol. 19: 133 (Vol. 138).
• Shu, M.H., Hung, W.J., Nguyen, T.L., Hsu, B.M., & Lu, C. (2014). Forecasting with Fourier residual modified ARIMA model-An empirical case of inbound tourism demand in New Zealand. WSEAS Transactions on Mathematics, 13(1), 12-21.
• Shu, M.H., Nguyen, T.L., Hsu, B., Lu, C., & Huang, J.C. (2014). Forecasting cargo throughput with modified seasonal ARIMA models. WSEAS Transactions on Mathematics, 13, 171-181.
• Soybilgen, B., (2015). Three essays on forecasting (PhD dissertation). Istanbul Bilgi Üniversitesi.
• Stock, J. H., Watson, M.W., (1999). Forecasting inflation. Journal of Monetary Economics, 44(2), 293-335.
• Tan, C.L., Chang, S.P., (1996). Residual correction method of Fourier series to GM(1,1) model. In Proceedings Of The First National Conference On Grey Theory And Applications, Kauhsiung, Taiwan (pp. 93-101).
• Tan, C.L., Lu, B.F., (1996). Grey Markov chain forecasting model. In Proceedings Of The First National Conference On Grey Theory And Applications, Kauhsiung, Taiwan (pp. 157-162).
• Tay Bayramoğlu, A., Öztürk, Z., (2017). ARIMA ve gri sistem modelleri ile enflasyon tahmini. Itobiad: Journal of the Human & Social Science Researches, 6(2).
• TCMB, (2020). Türkiye Cumhuriyet Merkez Bankası, Fiyat İstikrarı ve Enflasyon. Date Of Access: 10.01.2020.https://www.tcmb.gov.tr/wps/wcm/connect/TR/TCMB+TR/Main+Menu/Temel+Faaliyetler/Para+Politikasi/Fiyat+Istikrari+ve+Enflasyon/ Erişim Tarihi: 01.04.2020.
• Thakur, G.S.M., Bhattacharyya, R., Mondal, S.S., (2016). Artificial neural network based model for forecasting of inflation in India. Fuzzy Information and Engineering, 8(1), 87-100.
• Uğurlu, E., Saraçoğlu, B., (2010). Türkiye’de enflasyon hedeflemesi ve enflasyonun öngörüsü. Dokuz Eylül Üniversitesi İktisadi İdari Bilimler Fakültesi Dergisi, 25(2), 57-72.
• Wang, Y., Wang, J., Zhao, G., & Dong, Y. (2012). Application of residual modification approach in seasonal ARIMA for electricity demand forecasting: A case study of China. Energy Policy, 48, 284-294.
• Wen, K.L., 2004. Grey systems. Tucson, USA: Yang’s Scientific Press.
• Wu, L., Liu, S., Liu, D., Fang, Z., and Xu, H. (2015). Modelling and forecasting CO2 emissions in the BRICS (Brazil, Russia, India, China, And South Africa) countries using a novel multi-variable Grey model. Energy, 79, 489-495.