Nonlinear Chaotic Analysis of USD/TRY and EUR/TRY Exchange Rates

Öz

In this work USD/TRY and EUR/TRY Exchange rates are analyzed with nonlinear and chaotic time series analysis methods. In this work to detect chaos methods such as correlation dimension, Lyapunov exponent and surrogate data testing are utilized and obtained evidence for chaos in these exchange rates. Additionally, by utilizing recurrence quantification analysis (RQA) and cross utilizing recurrence quantification analysis (CRQA) it is demonstrated how chaotic properties of the exchange rates are change through time. In this study, it has been shown that RQA measures such as determinism, laminarity and entropy exhibited a steady decline after 2014. This decline indicates that the exchange rate market has become more unpredictable, more irregular and more unstable after 2014.

Anahtar Kelimeler

• Exchange Rates
• Chaos Theory
• Lyapunov Exponent
• Surrogate Data Testing
• Recurrence Quantification Analysis

DOLAR/TL ve EURO/TL Döviz Kurlarının Doğrusal Olmayan ve Kaotik Analizi

Öz

Bu çalışmada DOLAR/TL ve EURO/TL döviz kurları doğrusal olmayan ve kaotik zaman serileri analizi yöntemleriyle analiz edilmiştir. Bu çalışmada kaosun tespiti için korelasyon boyutu, Lyapunov katsayısı, vekil veri testi yöntemleri kullanılmış ve DOLAR/TL ve EURO/TL döviz kurlarında kaosun bulunduğuna dair kanıtlar elde edilmiştir. Ayrıca yineleme niceleme analizi (YNA) ve çapraz yineleme niceleme analizi (ÇYNA) yöntemleri kullanılarak döviz kurlarının kaotik özelliklerinin zaman içinde nasıl değiştiği gösterilmiştir. Bu çalışmada 2014 yılından sonra determinizm, laminarite ve entropi gibi YNA ölçütlerinin istikrarlı bir düşüş sergilediği gösterilmiştir. Bu düşüş 2014’ten sonra döviz kuru piyasasının daha öngörülemez, daha düzensiz ve daha kararsız hale geldiğini göstermektedir.

Anahtar Kelimeler

• Döviz Kurları
• Kaos Teorisi
• Lyapunov Katsayısı
• Vekil Veri Testi
• Yineleme Niceleme Analizi

Kaynakça

1. Adrangi, B., Allender, M. A., Chatrath, A., & Raffiee, K. (2010), Nonlinear dependencies and chaos in the bilateral exchange rate of the dollar. International Business & Economics Research Journal (IBER), Vol. 9, No. 3: 85-96.
2. Bajo-Rubio, O., Fernandez-Rodriguez, F., & Sosvilla-Rivero, S. (1992), Chaotic behavior in exchange-rate series: First results for the Peseta—US dollar case. Economics Letters, Vol. 39, No. 2: 207-211.
3. Bask, M. (2002), A positive Lyapunov exponent in Swedish exchange rates?. Chaos, Solitons & Fractals, Vol. 14, No. 8: 1295-1304.
4. Bastos, J. A., & Caiado, J. (2011), Recurrence quantification analysis of global stock markets. Physica A: Statistical Mechanics and its Applications, Vol. 390, No. 7: 1315-1325.
5. Belaire-Franch, J., Contreras, D., & Tordera-Lledó, L. (2002), Assessing nonlinear structures in real exchange rates using recurrence plot strategies. Physica D: Nonlinear Phenomena, Vol. 171, No. 4: 249-264.
6. Brock, W. A. (1986), Distinguishing random and deterministic systems: Abridged version. Journal of Economic Theory, Vol. 40, No. 1: 168-195.
7. Coco, M. I., & Dale, R. (2014), Cross-recurrence quantification analysis of categorical and continuous time series: an R package. arXiv preprint arXiv:1310.0201. doi:10.3389/fpsyg.2014.00510
8. Das, A., & Das, P. (2007), Chaotic analysis of the foreign exchange rates. Applied Mathematics and Computation, Vol. 185, No. 1: 388-396.

9. Eckmann, J. P., Kamphorst, S. O., & Ruelle, D. (1987), Recurrence Plots of Dynamical Systems. Europhysics Letters (EPL), Vol. 4, No. 9: 973-977. doi:10.1209/0295-5075/4/9/004
10. Faggini, M. (2014), Chaotic time series analysis in economics: balance and perspectives. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 24, No. 4: 042101. doi:10.1063/1.4903797
11. Faggini, M., Bruno, B., & Parziale, A. (2019), Does chaos matter in financial time series analysis?. International Journal of Economics and Financial Issues, Vol. 9, No. 4: 18-24.
12. Gilmore, C. G. (2001), An examination of nonlinear dependence in exchange rates, using recent methods from chaos theory. Global Finance Journal, Vol. 12, No. 1: 139-151.
13. Grassberger, P., & Procaccia, I. (1983), Measuring the strangeness of strange attractors. Physica. D, Vol. 9, No. 1-2: 189-208.
14. Huffaker, R. G., Huffaker, R., Bittelli, M., & Rosa, R. (2017), Nonlinear time series analysis with R. Oxford: Oxford University Press.
15. Kugiumtzis, D. (1997), Assessing different norms in nonlinear analysis of noisy time series. Physica D: Nonlinear Phenomena, Vol. 105, No. 1-3: 62-78.
16. Liu, L. (2009), Testing for Nonlinearity and Chaoticity in Exchange Rate Time Series, SEI online.
17. Lorenz, E. N. (1965), A study of the predictability of a 28-variable atmospheric model. Tellus, Vol. 17, No. 3: 321-333.
18. Marwan, N., & Kurths, J. (2002), Nonlinear Analysis of Bivariate Data with Cross Recurrence Plots. Physics Letters A, Vol. 302, No. 5-6: 299-307. doi:10.1016/s0375-9601(02)01170-2
19. Marwan, N., Thiel, M., & Nowaczyk, N. R. (2002), Cross recurrence plot based synchronization of time series. Nonlinear Processes in Geophysics, Vol. 9, No. 3/4: 325-331.
20. Moloney, K., & Raghavendra, S. (2012), Examining the dynamical transition in the Dow Jones Industrial. Physics Letters A, Vol. 223, No. 4: 255-260.
21. Piskun, O., & Piskun, S. (2011), Recurrence quantification analysis of financial market crashes and crises. arXiv preprint arXiv:1107.5420. http://arxiv.org/abs/1107.5420
22. Rosenstein, M. T., Collins, J. J., & De Luca, C. J. (1993), A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, Vol. 65, No. 1-2: 117-134.
23. Schreiber, T., & Schmitz, A. (2000), Surrogate time series. Physica D: Nonlinear Phenomena, Vol. 142, No. 3-4: 346-382.
24. Schwartz, B., & Yousefi, S. (2003), On complex behavior and exchange rate dynamics. Chaos, Solitons & Fractals, Vol. 18, No. 3: 503-523.
25. Serletis, A., & Gogas, P. (1997), Chaos in East European black market exchange rates. Research in Economics, Vol. 51, No. 4: 359-385.
26. Sewell, S. P., Stansell, S. R., Lee, I., & Below, S. D. (1996), Using chaos measures to examine international capital market integration. Applied Financial Economics, Vol. 6, No. 2: 91-101.
27. Soloviev, V., Serdiuk, O., Semerikov, S., & Kiv, A. (2020), Recurrence plot-based analysis of financial-economic crashes. CEUR Workshop Proceedings.
28. Strozzi, F., Zaldívar, J. M., & Zbilut, J. P. (2007), Recurrence quantification analysis and state space divergence reconstruction for financial time series analysis. Physica A: Statistical Mechanics and Its Applications, Vol. 376: 487-499.
29. Strozzi, F., Gutierrez, E., Noè, C., Rossi, T., Serati, M., & Zaldívar, J. M. (2008), Measuring volatility in the nordic spot electricity market using recurrence quantification analysis. The European Physical Journal Special Topics, Vol. 164, No. 1: 105-115.
30. Stutzer, M. J. (1980), Chaotic dynamics and bifurcation in a macro model. Journal of Economic Dynamics and Control, Vol. 2: 353-376.
31. Takens, F. (1981), Detecting Strange Attractors in Turbulence. In R. D. & Y. L.S. (Eds.), Dynamical Systems and Turbulence (pp. 366-381). Berlin, Heidelberg: Springer.
32. Theiler, J. (1990), Estimating the fractal dimension of chaotic time series. Lincoln Laboratory Journal, Vol. 3: 63-86.
33. Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Farmer, J. D. (1992), Testing for nonlinearity in time series: the method of surrogate data. Physica D: Nonlinear Phenomena, Vol. 58, No. 1-4: 77-94.
34. Torkamani, M. A., Mahmoodzadeh, S., Pourroostaei, S., & Lucas, C. (2007), Chaos theory and application in foreign exchange rates vs. IRR (Iranian Rial). International Journal of Human and Social Sciences, Vol. 1, No. 3: 130-134.
35. Xing, Y., & Wang, J. (2020), Linkages between global crude oil market volatility and financial market by complexity synchronization. Empirical Economics, Vol. 59, No. 5: 2405-2421.
36. Wallot, S. (2019), Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA)–a method for quantifying correlation between multivariate time-series. Multivariate Behavioral Research, Vol. 54, No. 2: 173-191.
37. Wallot, S., & Leonardi, G. (2018), Analyzing multivariate dynamics using cross-recurrence quantification analysis (crqa), diagonal-cross-recurrence profiles (dcrp), and multidimensional recurrence quantification analysis (mdrqa)–a tutorial in r. Frontiers in Psychology, Vol. 9: 2232. doi: 10.3389/fpsyg.2018.02232
38. Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985), Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, Vol. 16, No. 3: 285-317.
39. Zbilut, J. P. (2005), Use of Recurrence Quantification Analysis in Economic Time Series. In M. Salzano & A. Kirman (Eds.), Economics: Complex Windows (pp. 91-104). Milano: Springer.
40. Zbilut, J. P., & Webber, C. L. (1992). Embeddings and Delays as Derived from Quantification of Recurrence Plots. Physics Letters A, Vol. 171, No. 3-4: 199-203. doi:10.1016/0375-9601(92)90426-m