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An Application on Borsa Istanbul (BIST) Using Models Modified with Fourier Series

Year 2022, Volume: 5 Issue: 2, 81 - 91, 11.01.2023

Cebeli İnan , Erkan Oktay

Abstract

Predicting the future accurately is of vital importance in all disciplines, as well as in the field of social sciences. Especially today, due to the development of technology and the presence of package programs that can process huge data, it is a very important development for all fields, including econometrics, that we can reach more accurate estimates. As a result, it is a situation that is directly related to the decrease in the error rates of the forecasts and more accurate planning for the future. In this study, time series analyzes were made over the proportional changes of the closing values of the Borsa Istanbul (BIST30) index, that is, the monthly average closing values, and 24-month forecasts were calculated. For this purpose, in order to increase the accuracy of the prediction results of the classical ARIMA models and the models based on the Box-Cox transform, new prediction results were obtained with the models modified with the Fourier series. Mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE) and mean absolute percent error (MAPE) performance criteria were used to evaluate the success of the established models. It was concluded that the model with the lowest value for MSE, RMSE, MAE and MAPE performance criteria was more successful than the other models. As a result, more successful results were obtained with more accurate estimation results, that is, with lower error rates.

Keywords

ARIMA-Fourier BATS TBATS Time Series Stocks

References

  • Badr, A., Makarovskikh, T., Mishra, P., Abotaleb, M., Al Khatib, A. M. G., Karakaya, K., ... ve Attal, E. (2021). Modelling and forecasting of web traffic using Holt's linear, bats and TBATS models. J. Math. Comput. Sci., 11(4), 3887-3915.
  • Naim, I., Mahara, T., ve Idrisi, A. R. (2018). Effective short-term forecasting for daily time series with complex seasonal patterns. Procedia computer science, 132, 1832-1841.
  • Kulkarni, M., Jadha, A., ve Dhingra, D. (2020, March). Time Series Data Analysis for Stock Market Prediction. In Proceedings of the International Conference on Innovative Computing ve Communications (ICICC). (March 28, 2020). http://dx.doi.org/10.2139/ssrn.3563111
  • Hyndman, R. J., ve Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R. Journal of statistical software, 27(1), 1-22.
  • Kourentzes, N. (2019). nnfor: Time Series Forecasting with Neural Networks. R package version 0.9.6. https://CRAN.R-project.org/package=nnfor.
  • R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
  • Ollech D. (2021). seastests: Seasonality Tests. R package version 0.15.4. https://CRAN.R-project.org/package=seastests.
  • De Livera, A. M., Hyndman, R. J., ve 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/10.1198/jasa.2011.tm09771
  • Iwok, I. A., ve 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.
  • Walker, J. S. (1991). Fourier Series, Oxford University Press, New York.
  • Nachane, D., ve Clavel, J. G. (2008). “Forecasting interest rates: a comparative assessment of some second-generation nonlinear models.” Journal of Applied Statistics, 35(5), 493-514. https://doi.org/10.1080/02664760701835243
  • Hannan, E. J., Terrell, R. D., ve Tuckwell, N. E. (1970). “The seasonal adjustment of economic time series.” International Economic Review, 11(1), 24-52. https://doi.org/10.2307/2525336
  • Saeed, W. (2022). “Frequency-based ensemble forecasting model for time series forecasting.” Computational and Applied Mathematics, 41(2), 1-17. https://doi.org/10.1007/s40314-022-01765-x
  • Taylor, J. W. (2003). “Exponential smoothing with a damped multiplicative trend.” International journal of Forecasting, 19(4), 715-725. https://doi.org/10.1016/S0169-2070(03)00003-7
  • Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge Press. https://doi.org/10.1017/CBO9781107049994
  • Grinblatt, M., ve Keloharju, M. (2000). “The investment behavior and performance of various investor types: a study of Finland's unique data set.” Journal of financial economics, 55(1), 43-67. https://doi.org/10.1016/S0304-405X(99)00044-6
  • Cavanaugh, J. E. (1997). “Unifying the derivations for the Akaike and corrected Akaike information criteria.” Statistics ve Probability Letters, 33(2), 201-208. https://doi.org/10.1016/S0167-7152(96)00128-9
  • West, M., ve Harrison, J. (2006). Bayesian forecasting and dynamic models. Springer Science ve Business Media. Harvey, A. C. (1990). The econometric analysis of time series. Mit Press.
  • Akaike, H. (1974). “A new look at the statistical model identification.” IEEE transactions on automatic control, 19(6), 716-723. https://doi.org/10.1109/TAC.1974.1100705
  • Konarasinghe, W. G. S., Abeynayake, N. R., ve Gunaratne, L. H. P. (2015). “ARIMA models on forecasting Sri Lankan share market returns.” International journal of novel research in Physics Chemistry and Mathematics, 2(1), 6-12.
  • Hassani, H., Silva, E. S., Gupta, R., ve Segnon, M. K. (2015). “Forecasting the price of gold.” Applied Economics, 47(39), 4141-4152. https://doi.org/10.1080/00036846.2015.1026580
  • Asante-Darko, D., Adabor, E., ve Amponsah, S. K. (2016). “A Fourier series model for forecasting solid waste generation in the Kumasi metropolis of Ghana.” WIT Transactions on Ecology and the Environment, 202, 173-185. https://doi.org/10.2495/WM160161
  • Shu, M. H., Hung, W. J., Nguyen, T. L., Hsu, B. M., ve Lu, C. H. U. N. W. E. I. (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.
  • Mijinyawa, M., Mbaga, Y. V., Amdzaranda, M., ve Akinrefon, A. A. (2019). “Pairs Determination for Sine and Cosine Function in Modeling Nigerian Gross Domestic Product.” Direct Research Journal of Social Science and Educational Studies. 6 (6), 90-94.
  • Phumchusri, N., ve Ungtrakul, P. (2020). “Hotel daily demand forecasting for high-frequency and complex seasonality data: a case study in Thailand.” Journal of Revenue and Pricing Management, 19(1), 8-25. https://doi.org/10.1057/s41272-019-00221-6
  • Boudrioua, M. S., ve Boudrioua, A. (2020). “Modeling and forecasting the algerian stock exchange using the Box-Jenkins methodology.” Journal of Economics, Finance and Accounting Studies, 2(1), 1-15.
  • Leneenadogo, W., ve Pius, U. S. (2020). “A Comparative Study of Fourier Series Models and Seasonal-Autoregressive Integrated Moving Average Model of Rainfall Data in Port Harcourt.” Asian Journal of Probability and Statistics, 10(3): 36-46. https://doi.org/10.9734/ajpas/2020/v10i330249
  • Son, H. G., Kim, Y., ve Kim, S. (2020). “Time series clustering of electricity demand for industrial areas on smart grid.” Energies, 13(9), 2377. https://doi.org/10.3390/en13092377
  • Bağcı, B. (2020). “Hareketli ortalamalar ve üssel düzeltme yöntemlerinin tahmin gücünün artırılması: Türkiye’de döviz kuru tahmini” Turkuaz Uluslararası Sosyo-Ekonomik Stratejik Araştırmalar Dergisi, 2(2).
  • De Livera, A. ve Hyndman, R. (2009). “Forecasting time series with complex seasonal patterns using exponential smoothing.” Department of Econometrics ve Business Statistics, Monash University. Working paper 15/09

Fourier Serileri ile Modifiye Edilmiş Modelleri Kullanarak Borsa İstanbul (BİST) Üzerine Bir Uygulama

Year 2022, Volume: 5 Issue: 2, 81 - 91, 11.01.2023

Cebeli İnan , Erkan Oktay

Abstract

Bütün disiplinlerde geleceği doğru tahmin etme hayati öneme sahip olduğu gibi sosyal bilimler alanında da bu çok önemli bir durumdur. Özellikle günümüzde teknolojinin gelişmesi ve devasal verileri işleyebilecek paket programların olmasından ötürü daha doğru tahminlere ulaşabilmemiz ekonometri alanı dahil tüm alanlar için çok önemli bir gelişmedir. Sonuç olarak yapılan tahminlerin hata oranlarının azalması ve geleceğe dair daha doğru planlamaların yapılması ile direkt ilişkili bir durumdur. Bu çalışmada, Borsa İstanbul (BİST30) endeksi kapanış değerlerinin oransal değişimlerine yani, aylık ortalama kapanış değerleri üzerinden zaman serisi analizleri yapılmış ve 24 aylık öngörüler hesaplanmıştır. Bu amaçla klasik ARIMA modelleri ve Box-Cox dönüşümü temeline dayanan modellerin tahmin sonuçlarının doğruluklarını arttırmak için Fourier serileri ile modifiye edilmiş modeller ile yeni tahmin sonuçları elde edilmiştir. Kurulan modellerin başarısını değerlendirmek için ortalama kare hata (MSE), kök ortalama kare hata (RMSE), ortalama mutlak hata (MAE) ve ortalama mutlak yüzde hata (MAPE) performans ölçütleri kullanılmıştır. MSE, RMSE, MAE ve MAPE performans ölçütleri için en düşük değeri veren model diğer modellere göre daha başarılı olduğu sonucuna varılmıştır. Netice olarak yeni tahmin sonuçlarının daha doğru yani daha düşük hata oranları ile daha başarılı sonuçlar elde edilmiştir.

Keywords

ARIMA-Fourier Zaman Serileri Hisse Senetleri

References

  • Badr, A., Makarovskikh, T., Mishra, P., Abotaleb, M., Al Khatib, A. M. G., Karakaya, K., ... ve Attal, E. (2021). Modelling and forecasting of web traffic using Holt's linear, bats and TBATS models. J. Math. Comput. Sci., 11(4), 3887-3915.
  • Naim, I., Mahara, T., ve Idrisi, A. R. (2018). Effective short-term forecasting for daily time series with complex seasonal patterns. Procedia computer science, 132, 1832-1841.
  • Kulkarni, M., Jadha, A., ve Dhingra, D. (2020, March). Time Series Data Analysis for Stock Market Prediction. In Proceedings of the International Conference on Innovative Computing ve Communications (ICICC). (March 28, 2020). http://dx.doi.org/10.2139/ssrn.3563111
  • Hyndman, R. J., ve Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R. Journal of statistical software, 27(1), 1-22.
  • Kourentzes, N. (2019). nnfor: Time Series Forecasting with Neural Networks. R package version 0.9.6. https://CRAN.R-project.org/package=nnfor.
  • R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
  • Ollech D. (2021). seastests: Seasonality Tests. R package version 0.15.4. https://CRAN.R-project.org/package=seastests.
  • De Livera, A. M., Hyndman, R. J., ve 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/10.1198/jasa.2011.tm09771
  • Iwok, I. A., ve 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.
  • Walker, J. S. (1991). Fourier Series, Oxford University Press, New York.
  • Nachane, D., ve Clavel, J. G. (2008). “Forecasting interest rates: a comparative assessment of some second-generation nonlinear models.” Journal of Applied Statistics, 35(5), 493-514. https://doi.org/10.1080/02664760701835243
  • Hannan, E. J., Terrell, R. D., ve Tuckwell, N. E. (1970). “The seasonal adjustment of economic time series.” International Economic Review, 11(1), 24-52. https://doi.org/10.2307/2525336
  • Saeed, W. (2022). “Frequency-based ensemble forecasting model for time series forecasting.” Computational and Applied Mathematics, 41(2), 1-17. https://doi.org/10.1007/s40314-022-01765-x
  • Taylor, J. W. (2003). “Exponential smoothing with a damped multiplicative trend.” International journal of Forecasting, 19(4), 715-725. https://doi.org/10.1016/S0169-2070(03)00003-7
  • Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge Press. https://doi.org/10.1017/CBO9781107049994
  • Grinblatt, M., ve Keloharju, M. (2000). “The investment behavior and performance of various investor types: a study of Finland's unique data set.” Journal of financial economics, 55(1), 43-67. https://doi.org/10.1016/S0304-405X(99)00044-6
  • Cavanaugh, J. E. (1997). “Unifying the derivations for the Akaike and corrected Akaike information criteria.” Statistics ve Probability Letters, 33(2), 201-208. https://doi.org/10.1016/S0167-7152(96)00128-9
  • West, M., ve Harrison, J. (2006). Bayesian forecasting and dynamic models. Springer Science ve Business Media. Harvey, A. C. (1990). The econometric analysis of time series. Mit Press.
  • Akaike, H. (1974). “A new look at the statistical model identification.” IEEE transactions on automatic control, 19(6), 716-723. https://doi.org/10.1109/TAC.1974.1100705
  • Konarasinghe, W. G. S., Abeynayake, N. R., ve Gunaratne, L. H. P. (2015). “ARIMA models on forecasting Sri Lankan share market returns.” International journal of novel research in Physics Chemistry and Mathematics, 2(1), 6-12.
  • Hassani, H., Silva, E. S., Gupta, R., ve Segnon, M. K. (2015). “Forecasting the price of gold.” Applied Economics, 47(39), 4141-4152. https://doi.org/10.1080/00036846.2015.1026580
  • Asante-Darko, D., Adabor, E., ve Amponsah, S. K. (2016). “A Fourier series model for forecasting solid waste generation in the Kumasi metropolis of Ghana.” WIT Transactions on Ecology and the Environment, 202, 173-185. https://doi.org/10.2495/WM160161
  • Shu, M. H., Hung, W. J., Nguyen, T. L., Hsu, B. M., ve Lu, C. H. U. N. W. E. I. (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.
  • Mijinyawa, M., Mbaga, Y. V., Amdzaranda, M., ve Akinrefon, A. A. (2019). “Pairs Determination for Sine and Cosine Function in Modeling Nigerian Gross Domestic Product.” Direct Research Journal of Social Science and Educational Studies. 6 (6), 90-94.
  • Phumchusri, N., ve Ungtrakul, P. (2020). “Hotel daily demand forecasting for high-frequency and complex seasonality data: a case study in Thailand.” Journal of Revenue and Pricing Management, 19(1), 8-25. https://doi.org/10.1057/s41272-019-00221-6
  • Boudrioua, M. S., ve Boudrioua, A. (2020). “Modeling and forecasting the algerian stock exchange using the Box-Jenkins methodology.” Journal of Economics, Finance and Accounting Studies, 2(1), 1-15.
  • Leneenadogo, W., ve Pius, U. S. (2020). “A Comparative Study of Fourier Series Models and Seasonal-Autoregressive Integrated Moving Average Model of Rainfall Data in Port Harcourt.” Asian Journal of Probability and Statistics, 10(3): 36-46. https://doi.org/10.9734/ajpas/2020/v10i330249
  • Son, H. G., Kim, Y., ve Kim, S. (2020). “Time series clustering of electricity demand for industrial areas on smart grid.” Energies, 13(9), 2377. https://doi.org/10.3390/en13092377
  • Bağcı, B. (2020). “Hareketli ortalamalar ve üssel düzeltme yöntemlerinin tahmin gücünün artırılması: Türkiye’de döviz kuru tahmini” Turkuaz Uluslararası Sosyo-Ekonomik Stratejik Araştırmalar Dergisi, 2(2).
  • De Livera, A. ve Hyndman, R. (2009). “Forecasting time series with complex seasonal patterns using exponential smoothing.” Department of Econometrics ve Business Statistics, Monash University. Working paper 15/09
There are 30 citations in total.

Details

Primary Language Turkish
Subjects Economics
Journal Section Research Article
Authors

Cebeli İnan 0000-0002-7924-9911

Erkan Oktay 0000-0002-1739-3184

Early Pub Date January 11, 2023
Publication Date January 11, 2023
Submission Date August 16, 2022
Published in Issue Year 2022Volume: 5 Issue: 2

Cite

APA İnan, C., & Oktay, E. (2023). Fourier Serileri ile Modifiye Edilmiş Modelleri Kullanarak Borsa İstanbul (BİST) Üzerine Bir Uygulama. Turkish Research Journal of Academic Social Science, 5(2), 81-91.

ISSN: 2667-4491

20120

This work is licensed under Creative Commons Attribution 4.0 International License 

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Turkish Research Journal of Academic Social Science (TURAJAS) is indexed by the following national and international scientific indexing services:

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