Chaotic dynamics in Turkish foreign exchange markets
- Kaos, Lyapunov Katsayısı, Verimli Piyasalar Hipotezi, Sepet Kur, Türk Lirası
- Chaos, Lyapunov Exponent, Efficient Market Hypothesis, Exchange Rate, Turkish Lira
How to Cite
Copyright (c) 2022 Ata ÖZKAYA
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
The financial systems, and particularly foreign exchange markets, are complex. This study investigates whether the Turkish foreign exchange market exhibits chaotic dynamics. To achieve this goal, we focus on a currency basket composed of equally-weighted Euro and US Dollar against the Turkish Lira. We compute Lyapunov exponents (LE) embedded in daily data of the currency basket from 2018M05D01 to 2022M05D23. The time interval under examination also indicates Turkey's alternative economic and financial policies have been preferred. We employed the phase space reconstruction method, which enables the detection of multiple equilibria in foreign exchange markets due to recent monetary policy applications. The study's main findings demonstrate that the daily currency basket data exhibit chaotic behaviour, and the associated maximal Lyapunov exponent is positive. An increase in complexity may recursively cause volatility in exchange rates for some time interval. Therefore, in policy-making, finding the root factors that sustain the chaotic behaviour of exchange rates and preventing multiple equilibria on expectations is crucial, which leads back to volatility. The study findings have important implications for interventions of Central banks as well as portfolio and risk management.
- Abarbanel, H.D.I. (1995), Analysis of observed chaotic data, Springer.
- Abhyankar, A., Copeland,L.S., and Wong,W. (1997),.Uncovering non-linear structure in real time stock market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100. Journal of Business & Economic Statistics, 15(1), 1-14.
- Badshah, I.U., Frijns,B., and Tourani-Rad,A. (2013).Contemporaneous Spill-Over Among Equity, Gold, and Exchange Rate Implied Volatility Indices. Journal of Future Markets, 33: 555-572. https://doi.org/10.1002/fut.21600
- Bandi, F, and Reno,R. (2016).Price and volatility co-jumps. Journal of Financial Economics, 119, 107–146.
- Brock, W.A., Lakonishok,J., and LeBaron,B. (1992).Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance, 47, 1731–1764.
- Calvo, G. A. (1988). Servicing the public debt: The role of expectations. American Economic Review, American Economic Association, 78(4),647-661.
- Calvo,G. and Reinhart,C. (2002).Fear of floating. Quarterly Journal of Economics, 117, 379-408.
- Das, A., and Das, P. (2007). Chaotic analysis of the foreign exchange rates. Applied Mathematics and Computation, 185, 388–396.
- Eckmann, J.P.S., Kamphorst,S.O., Ruelle,D., and Scheinkman,J.A. (1988). Lyapunov Exponents for Stock Returns”, in The Economy as an Evolving Complex System, eds. P.W. Anderson, K.J.Arrow, and D. Pines, New York; Addison-Wesley, 301-304
- Edgar, E. P. (1991). A Chaotic Attractor for the S&P 500.Financial Analysts Journal, 47(2), 55-62.
- Ehrmann, M., Fratscher,M., and Rigobon,R. (2011).Stocks, bonds, money markets and exchange rates: Measuring international financial transmission. Journal of Applied Econometrics, 26, 948–974.
- Eldridge, R.M., and Coleman, M.P. (1993).The British FTSE-100 Index: Chaotically Deterministic or Random?, working paper, Fairfield University, School of Business
- Fama, E. F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. The Journal of Finance, 25(2), 383–417. https://doi.org/10.2307/2325486
- Gencay, R., and Dechert,W.D. (1992).Algorithm for the n Lyapunov exponents of an n-dimensional unknown dynamical system. Physica D, 59,142-157.
- Gencay, R. (1998). The predictability of security returns with simple technical trading rules.Journal of Empirical Finance,5, 347–359
- Grassberger, P., and Procaccia,I. (1983).Estimation of the Kolmogorov entropy from a chaotic signal. Physics Review A, 29:2591-3.
- Hagtvedt, R. (2009). Stock return dynamics and the CAPM anomalies.Applied Economics Letters, 16(16),1593-1596.
- Hegger, R., Kantz,H., and Schreiber,T. (1999).Practical implementation of non-linear time series methods: The TISEAN package. Chaos, 9, 413.
- Hsieh,D.A.(1993). Implications of Nonlinear Dynamics for Financial Risk Management. The Journal of Financial and Quantitative Analysis, 28 (1), 41–64 https://doi.org/10.2307/2331150.
- Jegadeesh, N. (1990). Evidence of predictable behaviour of security returns. Journal of Finance, 45,881–898.
- Kantz, H. (1994). A robust method to estimate the maximal Lyapunov exponent of a time series.Physics Letters A, 185, 77-87.
- Kodres, L.E., and Papell., D.H. (1991). Nonlinear Dynamics in the Foreign Exchange Futures Market, working paper, University of Michigan, School of Business and Administration.
- Lehmann, B.N. (1990). Fads, martingales and market efficiency. Quarterly Journal of Economics, 105, 1–28.
- Malkiel, B. G. (2003). The Efficient Market Hypothesis and Its Critics. Journal of Economic Perspectives, 17 (1): 59-82.
- Mishra,R.K., Sehgal,S., Bhanumurthy,N.R. (2011). A search for long-range dependence and chaotic structure in Indian stock market.Review of Financial Economics,20,2,96-104,
- Obstfeld, M., Shambaugh,J.C., and Taylor,A.M. (2005). The trilemma in history: tradeoffs among exchange rates, monetary policies, and capital mobility. The Review of Economics and Statistics, 87,423-438
- Oduncu, A., Akcelik,Y., Ermisoglu,E. (2013).Reserve Options Mechanism and FX Volatility.Working Papers 1303, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
- Ozkaya, A. (2015). A model of active trading by using the properties of chaos. Digital Signal Processing, (39),15-21,
- Panas, E. & Vassilia, N.(2000). Are oil markets chaotic? A non-linear dynamic analysis. Energy Economics,22(5), 549-568.
- Pesaran, M.H. (2010). Predictability of asset returns and the efficient market hypothesis. Cesifo working papers No.3116.
- Peters,E.E. (1991). A chaotic attractor for the S&P 500. Financial Analysis Journal, 47(2), 55–62.
- Quang, T.V. (2005). The Fractal Market Analysis nad Its Application on Czech Conditions. Acta Oeconomica Pragensia, 101-111.
- Scheinkman, J.A., and LeBaron, B. (1989). Nonlinear Dynamics and Stock Returns. Journal of Business, 62, 311-337.
- Serletis,A., and Dormaar, P. (1996). Testing for deterministic non-linear dependence in the australian dollar-US exchange rate series. Applied Economics Letters, 3(4), 267-269.
- Rigobon, R. and Sack,B. (2003). Spillovers across U.S. financial markets. NBER Working paper, Vol. 9640, Cambridge, MA.
- Takens, F. (1981). Detecting Strange Attractors in Turbulence, in Dynamical Systems and Turbulence. Lecture Notes in Mathematics, 898, Berlin: Springer-Verlag, 366-381.
- Tiwari,A.K. and Gupta,R.R. (2019).Chaos in G7 stock markets using over one century of data: A note. Research in International Business and Finance,47,304-310,
- Todorov, V. and Tauchen,G. (2011). Volatility jumps. Journal of Business and Economics Statistics, 29, 356–371.
- Vaidyanathan, R. and Krehbiel,T. (1992) .Does the S&P 500 Futures Mispricing Series Exhibit Nonlinear Dynamics Dependence Across Time? Journal of the Future Market, 12, 659-677.
- Vassilicos, J.C., Demos, A., and Tata, F. (1992), No Evidence of Chaos but Some Evidence of Multifractals in the Foreign Exchange and the Stock Markets, Discussion Paper 143, Financial Markets Group Discussion Paper Series, London School of Economics.
- Vasilios P., Rangan,G., Gil-Alana,L.A., and Wohar,M.E. (2019).Are BRICS exchange rates chaotic? Applied Economics Letters, 26:13, 1104-1110, DOI: 10.1080/13504851.2018.1537473
- Wolf, A., Swift,J.B., Swinney,H.L., and Vastano,J.A. (1985).Determining Lyapunov Exponents from a time series. Physica D,16(3)