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DOI :10.26650/ekoist.2022.37.1113670   IUP :10.26650/ekoist.2022.37.1113670    Full Text (PDF)

Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models

Yakup Arı

This paper aims to make a comparison between range-based and return-based volatility models. For this purpose, we compare the Conditional Autoregressive Range (CARR) type and Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models with different innovation distributions and the Exponential Weighted Moving Average (EWMA) model with fixed and estimated lambda parameters. The out-of-sample forecasts obtained from the volatility processes are compared according to the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Heteroskedastic Root Mean Square Error (HRMSE), and Heteroskedastic Mean Absolute Error (HMAE) statistics. We use the USD-TRY exchange rate data for real-life applications since estimating the volatility of forex helps to determine prices for goods and services to avoid the uncertainty created by exchange rate shocks in developing countries such as Turkiye. Although MAE and RMSE show Gumbel CARR and Weibull CARR have the minimum error statistics, respectively, the HMAE and HRMSE statistics indicate that among the range-based models, the EWMA model, in which the lambda parameter is estimated, performs better. Furthermore, we find that Exponential CARR according to RMSE and MAE statistics, and Weibull CARR according to HMAE and HRMSE statistics appear as the return-based volatility models with minimum error.

Keywords: CARR, EWMA, GARCH, Volatility, USD-TRY

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References

  • Andersen, T. G., Bollerslev, T., & Lange, S. (1999). Forecasting financial market volatility: Sample frequency vis-à-vis forecast horizon. Journal of Empirical Finance, 6(5), 457-477. doi:10.1016/ s0927-5398(99)00013-4 google scholar
  • Arı, Y. (2020). From Discrete to Continuous: GARCH Volatility Modelling with R. Retrieved from https://math-stat.net/garch-and-cogarch-modelling.htm google scholar
  • Arı, Y. (2021a). Volatility spillovers effect analysis during Covid-19 period using EWMA model: The case of health sector stocks in ISE. Ömer Halisdemir Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi , 14 (4) , 1453-1467 . DOI: 10.25287/ohuiibf.917674 google scholar
  • Arı, Y. (2021b). Engle-Granger Cointegration Analysis Between Garch-Type Volatilities of Gold and Silver Returns. Alanya Akademik Bakış, 5 (2), 589-618. Doi: 10.29023/alanyaakademik.838284 google scholar
  • Bayracı, S., & Unal, G. (2014). Stochastic interest rate volatility modeling with a continuous-time GARCH(1, 1) model. Journal of Computational and Applied Mathematics, 259, 464-473. doi:10.1016/j.cam.2013.10.017 google scholar
  • Bollen, B. (2014). What should the value of lambda be in the exponentially weighted moving average volatility model? Applied Economics, 47(8), 853-860. doi:10.1080/00036846.2014.98285 google scholar
  • Bollerslev, T. P. (1986). Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics, 31, pp. 307-327. google scholar
  • Bollerslev, T. (2010) Glossary to ARCH (GARCH*), in Volatility and Time Series Econometrics: Essays in Honor of Robert Engle, Bollerslev, T., Russell, J. and Watson, M. (Eds). doi:10.1093/ acprof:oso/ 9780199549498.001.0001 google scholar
  • Chiang, M.-H., Chou, R. Y., & Wang, L.-M. (2014). Outlier Detection in the Lognormal Logarithmic Conditional Autoregressive Range Model. Oxford Bulletin of Economics and Statistics, 78(1), 126-144. doi:10.1111/obes.12081 google scholar
  • Chou, R. Y. (2005). Forecasting financial volatilities with extreme values: the conditional autoregressive range (CARR) model. Journal of Money, Credit and Banking, Vol. 37, pp. 561-582. google scholar
  • Chou, R. (2006). Modeling the asymmetry of stock movements using price ranges. Advances in Econometrics, 20, 231-257. google scholar
  • Demiralay, S. & Bayraci, S. (2015) Central and Eastern European Stock Exchanges under Stress: A Range-Based Volatility Spillover Framework. Finance a Uver: Czech Journal of Economics & Finance. Vol. 65 Issue 5, p411-430. google scholar
  • Ding Z., Engle R.F. and Granger C.W.J. (1993). A long memory property of stock market return and a new model, Journal of Empirical Finance 1(1), 83-106. google scholar
  • Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50 (4), pp. 987-1007 google scholar
  • Engle, R. F., & Bollerslev T. (1986). Modelling the persistence of conditional variances. Econometric Reviews 5: 1-50. google scholar
  • Engle, R. F., & Russell, J. R. (1998). Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data. Econometrica, 66(5), 1127. doi:10.2307/2999632 google scholar
  • Ghalanos, A. (2020a). rugarch: Univariate GARCH models. R package version 1.4-2. Available at: https://cran.r-project.org/rugarch.pdf google scholar
  • Ghalanos, A. (2020b). Introduction to the rugarch package. Technical Report Available at: Introduction_to_the_rugarch_package.pdf google scholar
  • Glosten L.R, Jagannathan R. and Runkle D.E. (1993). Relationship between the expected value and the volatility of the nominal excess return on stocks, The Journal of Finance,48(5), 1779-1801. google scholar
  • Hentschel, L. (1995). All in the family Nesting symmetric and asymmetric GARCH models. Journal of Financial Economics, 39(1), 71-104. doi:10.1016/0304-405x(94)00821-h google scholar
  • Higgins, M. L., and Anil. K. B. (1992). A Class of Nonlinear ARCH Models. International Economic Review 33: 137-58. google scholar
  • Hull, J. C. (2018). Options, Futures, & Other Derivatives, Ninth Edition, Global Edition, Pearson Education Limited.,England google scholar
  • Markowitz, H. (1952). Portfolio Selection*. The Journal of Finance, 7: 77-91. https://doi. org/10.1111/j.1540-6261.1952.tb01525.x google scholar
  • Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach, Econometrica 59: 347-370. google scholar
  • Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. Journal ofBusiness, 53, 61-65. google scholar
  • Poon, S.-H., & Granger, C. W. J. (2003). Forecasting Volatility in Financial Markets: A Review. Journal of Economic Literature, 41(2), 478-539. doi:10.1257/002205103765762743 google scholar
  • Poon, S.-H., & Granger, C. (2005). Practical Issues in Forecasting Volatility. Financial Analysts Journal, 61(1), 45-56. doi:10.2469/faj.v61.n1.2683 google scholar
  • Ratnayake, M.I.P.R. (2021). Modeling time series with conditional heteroscedastic structure. Unpublished Ph.D. Dissertation. Missouri University, USA. google scholar
  • Riskmetrics Technical Document (1996) 4th edn, J. P. Morgan. Available at http://yats.free.fr/ papers/td4e.pdf (accessed 12 December 2021). google scholar
  • Quiros, J.L., & Izquierdo, J.D. (2011). Volatility forecasting with range models: An evaluation of new alternatives to the CARR model. Available at https://repositorio.ipl.pt google scholar
  • Schwert, G. W. (1990). Stock volatility and the crash of ’87. Review of Financial Studies 3: 103-6. google scholar
  • Taylor S. (1986). Modelling Financial Time Series, Wiley, New York. google scholar
  • Tsay, R.S. (2009). Autoregressive Conditional Duration Models. In: Palgrave Handbook of Econometrics. Springer, pp. 1004-1024. google scholar
  • Tsay, R. S. (2012). An Introduction to Analysis ofFinancial Data with R (1st ed.). Wiley. google scholar
  • Tsay, R. S. (2013). Multivariate Time Series Analysis: With R and Financial Applications (1st ed.). Wiley. google scholar
  • Unstarched. (2014, July 6). The EWMA model. http://www.unstarched.net/r-examples/rugarch/the-ewma-model/(accessed 12 December 2021). google scholar
  • Xie H. (2018). Financial volatility modeling: The feedback asymmetric conditional autoregressive range model. Journal ofForcasting. 38:11-28. google scholar
  • Xie, H., & Wu, X. (2017). A conditional autoregressive range model with gamma distribution for financial volatility modelling. Economic Modelling, 64, 349-356. google scholar
  • Zakoian, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18: 931-55 google scholar

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APA

Arı, Y. (2022). Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models. Ekoist: Journal of Econometrics and Statistics, 0(37), 107-127. https://doi.org/10.26650/ekoist.2022.37.1113670


AMA

Arı Y. Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models. Ekoist: Journal of Econometrics and Statistics. 2022;0(37):107-127. https://doi.org/10.26650/ekoist.2022.37.1113670


ABNT

Arı, Y. Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models. Ekoist: Journal of Econometrics and Statistics, [Publisher Location], v. 0, n. 37, p. 107-127, 2022.


Chicago: Author-Date Style

Arı, Yakup,. 2022. “Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models.” Ekoist: Journal of Econometrics and Statistics 0, no. 37: 107-127. https://doi.org/10.26650/ekoist.2022.37.1113670


Chicago: Humanities Style

Arı, Yakup,. “Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models.” Ekoist: Journal of Econometrics and Statistics 0, no. 37 (Mar. 2023): 107-127. https://doi.org/10.26650/ekoist.2022.37.1113670


Harvard: Australian Style

Arı, Y 2022, 'Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models', Ekoist: Journal of Econometrics and Statistics, vol. 0, no. 37, pp. 107-127, viewed 22 Mar. 2023, https://doi.org/10.26650/ekoist.2022.37.1113670


Harvard: Author-Date Style

Arı, Y. (2022) ‘Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models’, Ekoist: Journal of Econometrics and Statistics, 0(37), pp. 107-127. https://doi.org/10.26650/ekoist.2022.37.1113670 (22 Mar. 2023).


MLA

Arı, Yakup,. “Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models.” Ekoist: Journal of Econometrics and Statistics, vol. 0, no. 37, 2022, pp. 107-127. [Database Container], https://doi.org/10.26650/ekoist.2022.37.1113670


Vancouver

Arı Y. Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models. Ekoist: Journal of Econometrics and Statistics [Internet]. 22 Mar. 2023 [cited 22 Mar. 2023];0(37):107-127. Available from: https://doi.org/10.26650/ekoist.2022.37.1113670 doi: 10.26650/ekoist.2022.37.1113670


ISNAD

Arı, Yakup. “Chasing Volatility of USD/TRY Foreign Exchange Rate: The Comparison of CARR, EWMA, and GARCH Models”. Ekoist: Journal of Econometrics and Statistics 0/37 (Mar. 2023): 107-127. https://doi.org/10.26650/ekoist.2022.37.1113670



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Submitted07.05.2022
Accepted03.11.2022
Published Online29.12.2022

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