ARMA-GARCH Yaklaşımıyla USD/TRY Döviz Kurunun Modellenmesi ve Tahmini

Öz

Döviz kuru fiyatlarının doğru bir şekilde tahmin edilmesi, yatırımcıların döviz kuru yatırımlarından maksimum kazanç elde etmelerine ve döviz kurları ile iş yapan firmaların bu tahminlere göre ticaretlerini yönetmelerine yardımcı olur. Bu nedenle döviz kuru fiyatlarının tahmini, hem yatırımcılar hem de döviz kurlarıyla iş yapan şirketler için çok önemlidir. Bu çalışmada, döviz kuru fiyatlarını modellemek için çeşitli GARCH (Genelleştirilmiş Otoregresif Koşullu Değişken Varyans) modelleri ile birleştirilmiş ARMA (Otoregresif Hareketli Ortalama) modelleri uygulanmıştır. Bu amaçla, volatilitenin döviz kuru fiyatları üzerindeki etkisini belirlemek için hataların hem simetrik hem de çarpık olarak dağıldığı ARMA-GARCH (M) modelleri ve ARMA-GARCH modelleri incelenmiştir. Uyum iyiliği ve tahmin doğruluğu performans kriterlerine göre belirlenen en uygun modelin, ilk olarak asimetrik ve doğrusal olmayan yapıları modelleyebilen ARMA-NAGARCH modeli ve ikinci olarak ise ARMA-GJRGARCH modeli olduğu sonucuna varılmıştır. Bununla birlikte ARMA-GARCH (M) modellerinin performansı, ARMA-GARCH modellerine göre daha düşük olması nedeniyle volatilitenin döviz kuru fiyatlarına etkisi zayıf bulunmuştur.

Anahtar Kelimeler

• ARIMA
• GARCH Modelleri
• Döviz Kuru
• Öngörü
• Model Değerlendirme

Modeling and Forecasting of USD/TRY Exchange Rate Using ARMA-GARCH Approach

Öz

Accurately predicting the exchange rate prices helps investors to obtain maximum profit from their exchange rate investments as well as to help firms conducting business with exchange rates to manage their trading based on these predictions. Therefore, the prediction of exchange rate prices is crucial for both investors and companies engaged in exchange rates. In this study, ARMA (Autoregressive Moving Average) models combined with various GARCH (Generalized Autoregressive Conditional Heteroscedasticity) models are applied to model exchange rate prices. For this purpose, ARMA-GARCH (M) models are investigated in order to determine the effect of volatility on exchange rate prices as well as ARMA-GARCH models in which the errors are distributed both symmetrically and skewed. It is concluded that the best fitted model which is determined based on the goodness of fit and estimation accuracy performance criteria, is firstly ARMA-NAGARCH model which can model asymmetric and non-linear structures and secondly ARMA-GJRGARCH model. However, since the performance of ARMA-GARCH (M) models is lower than ARMA-GARCH models, the effect of volatility on exchange rate prices is found to be weak.

Anahtar Kelimeler

• ARIMA
• GARCH Models
• Exchange Rates
• Forecasting
• Model Evaluation

Kaynakça

1. Abdalla, S. Z. S., & Winker, P. (2012). Modelling stock market volatility using univariate GARCH models: Evidence from Sudan and Egypt. International Journal of Economics and Finance, 4(8), 161-176.
2. Abdullah, S. M., Siddiqua, S., Siddiquee, M. S. H., & Hossain, N. (2017). Modeling and forecasting exchange rate volatility in Bangladesh using GARCH models: a comparison based on normal and Student’s t-error distribution. Financial Innovation, 3(1), 1-19.
3. Agnolucci, P. (2009). Volatility in crude oil futures: a comparison of the predictive ability of GARCH and implied volatility models. Energy Economics, 31(2), 316-321.
4. Akaike, H. (1973). Information theory and extension of the maximum likelihood principle. In: Petrov, B.N., Cszaki, F. (Eds.), Second International Symposium on Information Theory. Akademiai Kiado, Budapest, pp. 267–281.
5. Atabani Adi, A. (2019). Modeling exchange rate return volatility of RMB/USD using GARCH family models. Journal of Chinese Economic and Business Studies, 17(2), 169-187.
6. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327.
7. Box, G. E. P., Jenkins, G. M., & Reinsel, G. C. (1994). Time series analysis, forecasting and control. Englewood Clifs.
8. Caporale, G. M., & Zekokh, T. (2019). Modelling volatility of cryptocurrencies using Markov-Switching GARCH models. Research in International Business and Finance, 48, 143-155.

9. de Oliveira, F. A., Nobre, C. N., & Zárate, L. E. (2013). Applying Artificial Neural Networks to prediction of stock price and improvement of the directional prediction index–Case study of PETR4, Petrobras, Brazil. Expert systems with applications, 40(18), 7596-7606.
10. Dritsaki, C. (2017). Modeling and forecasting of british pound/us dollar exchange rate: an empirical analysis. In International Conference on Applied Economics (pp. 437-455). Springer, Cham.
11. Efimova, O., & Serletis, A. (2014). Energy markets volatility modelling using GARCH. Energy Economics, 43, 264-273.
12. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 987-1007.
13. Engle, R. F., & Ng, V. K. (1993). Measuring and testing the impact of news on volatility. The journal of finance, 48(5), 1749-1778.
14. Epaphra, M. (2016). Modeling exchange rate volatility: Application of the GARCH and EGARCH models. Journal of Mathematical Finance, 7(1), 121-143.
15. Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The journal of finance, 48(5), 1779-1801.
16. Gupta, S., & Kashyap, S. (2016). Modelling volatility and forecasting of exchange rate of British pound sterling and Indian rupee. Journal of Modelling in Management, 11(2), 389-404.
17. Kang, S. H., & Yoon, S. M. (2013). Modeling and forecasting the volatility of petroleum futures prices. Energy Economics, 36, 354-362.
18. Lim, C. M., & Sek, S. K. (2013). Comparing the performances of GARCH-type models in capturing the stock market volatility in Malaysia. Procedia Economics and Finance, 5, 478-487.
19. Liu, H. C., & Hung, J. C. (2010). Forecasting S&P-100 stock index volatility: The role of volatility asymmetry and distributional assumption in GARCH models. Expert Systems with Applications, 37(7), 4928-4934.
20. Mohammadi, H., & Su, L. (2010). International evidence on crude oil price dynamics: Applications of ARIMA-GARCH models. Energy Economics, 32(5), 1001-1008.
21. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the Econometric Society, 347-370.
22. Pahlavani, M., & Roshan, R. (2015). The comparison among ARIMA and hybrid ARIMA-GARCH models in forecasting the exchange rate of Iran. International Journal of Business and Development Studies, 7(1), 31-50.
23. Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, 6(2), 461-464.
24. Teresiene, D. (2009). Lithuanian stock market analysis using a set of GARCH models. Journal of Business Economics and Management, 10(4), 349-360.
25. Yaziz, S. R., Azizan, N. A., Zakaria, R., & Ahmad, M. H. (2013, December). The performance of hybrid ARIMA-GARCH modeling in forecasting gold price. In 20th international congress on modelling and simulation, adelaide (pp. 1-6).
26. Zakoian, J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and control, 18(5), 931-955.