Economic Research and Perspectives

Economic Research and Perspectives

Nonlinear Dynamics and Chaotic Intensity of the USD–IRR Exchange Rate in Iran: Monetary Policy Implications (2009–2024)

Document Type : Original Research

Authors
Delara Mousavi 1
Ahmad Googerdchian 2
1 M.A. Graduate in Theoretical Economics, Faculty of Economics, University of Isfahan, Isfahan, Iran
2 Faculty Member and Associate Professor, Faculty of Economics, University of Isfahan, Isfahan, Iran
10.48311/ecor.2025.115447.0
Abstract
Abstract
Within complex systems, chaos theory demonstrates that even simple interactions can generate highly intricate structures and interdependent dynamics, whereby minor perturbations—analogous to the butterfly effect—may substantially alter a system’s trajectory. The Iranian foreign exchange market represents such a nonlinear system, in which macroeconomic policies, geopolitical developments, and market expectations interact to produce behaviors that cannot be adequately explained by classical equilibrium-based frameworks. This study applies a comprehensive suite of nonlinear dynamical system techniques—including the Brock–Dechert–Scheinkman (BDS) test, Lyapunov exponents, fractal dimensions, the Hurst exponent, phase-space reconstruction, Poincaré maps, Kolmogorov–Sinai entropy, and the zero–one test for chaos—to examine the intrinsic dynamics of the USD–IRR exchange rate from 2009 to 2024. The analysis seeks to identify fundamental sources of instability and quantify the degree of chaoticity, independently of transient external shocks or superficial fluctuations. Comparative evaluation indicates that chaotic intensity varies systematically across monetary policy regimes and geopolitical contexts. Periods of heightened chaos coincide with abrupt currency surges and institutional uncertainty, whereas relatively stable intervals correspond to lower entropy, moderated chaotic behavior, and greater informational coherence. These findings offer a holistic characterization of the market’s intrinsic complexity and underscore the necessity of nonlinear, multi-metric analytical frameworks for understanding exchange rate dynamics and informing effective economic policy.
Purpose/Aims:
This study aims to systematically investigate the chaotic and complex dynamics of Iran’s USD–IRR exchange rate by disentangling endogenous fluctuations from exogenous disturbances. By quantifying chaotic intensity, identifying multifractal structures, and uncovering latent instability mechanisms, the research seeks to deepen understanding of currency market behavior in a politically sensitive emerging economy. Ultimately, the study aspires to generate policy-relevant insights for designing adaptive, complexity-aware interventions that acknowledge the irreducible uncertainty inherent in nonlinear financial systems.
Methodology & Framework:
A hybrid analytical framework integrating chaos theory with advanced nonlinear dynamical system methods was employed. Daily USD–IRR exchange rate data covering 2009–2024 were analyzed using complementary quantitative metrics to capture both temporal and structural complexity.
The BDS test was applied to detect nonlinearity and assess the adequacy of linear stochastic specifications. Lyapunov exponents were estimated to quantify sensitivity to infinitesimal perturbations and evaluate the presence of deterministic chaos. Fractal dimension analysis was conducted to detect multifractal structures, while the Hurst exponent was calculated to assess long-range dependence. Phase-space reconstruction and Poincaré maps were used to visualize the underlying system geometry and identify recurrent dynamic patterns.
Entropy-based measures—including Kolmogorov–Sinai entropy and permutation entropy—were computed to quantify information production and intrinsic disorder. Finally, the zero–one test for chaos was implemented to validate deterministic chaotic dynamics and ensure robustness against stochastic artifacts.
This integrated methodological design enables a multidimensional assessment of exchange rate behavior, combining dynamical, geometrical, and informational indicators while mitigating potential biases associated with reliance on a single technique.
Findings:
The empirical results demonstrate that the Iranian exchange rate exhibits pronounced chaotic dynamics and substantial sensitivity to initial conditions. Positive Lyapunov exponents (λ ≈ 0.53) indicate rapid amplification of minor perturbations, confirming deterministic chaos. Estimated fractal dimensions (D₂ ≈ 1.34–1.57) reveal heterogeneous multifractal structures, and the Hurst exponent (H ≈ 0.56–0.62) indicates persistent long-term memory.
Entropy measures reflect significant information generation, consistent with endogenous complexity and inherent unpredictability. Comparative analysis across distinct monetary policy regimes suggests that chaotic intensity increases during politically turbulent or interventionist periods, coinciding with abrupt exchange rate movements and heightened uncertainty. In contrast, relatively stable intervals are characterized by lower entropy, moderated chaoticity, and comparatively greater predictability.
Discussion:
The USD–IRR exchange rate appears to be driven primarily by internal feedback mechanisms, heterogeneous agent interactions, and nonlinear adjustment processes rather than by exogenous shocks alone. These findings are broadly consistent with international research documenting chaotic features in exchange rate dynamics, while also providing context-specific insights into the structural and institutional characteristics of Iran’s foreign exchange market.
The evidence suggests that conventional linear or equilibrium-based models substantially underestimate the system’s complexity. Accordingly, advanced nonlinear analytical frameworks are essential for both empirical investigation and policy formulation in environments characterized by structural fragility and geopolitical sensitivity.
Conclusion & Implications:
The Iranian foreign exchange market operates as a chaotic, self-organizing system exhibiting pronounced sensitivity to initial conditions and persistent multifaceted fluctuations. Endogenous nonlinear feedback loops play a dominant role in shaping its evolution, thereby constraining long-term predictability.
Effective monetary and regulatory strategies must therefore adopt adaptive, complexity-aware approaches. Such strategies may include real-time monitoring of chaos-sensitive indicators, phase-dependent policy calibration, and entropy-informed evaluation of market conditions. Calibrating interventions according to observed levels of chaotic intensity—ranging from incremental adjustments during relatively stable periods to coordinated regulatory responses during severe turbulence—may enhance systemic resilience, mitigate risk transmission, and support market confidence.
This study contributes both methodologically and substantively to the analysis of exchange rate dynamics in emerging and geopolitically sensitive economies, demonstrating that understanding and managing nonlinear complexity is indispensable for sustaining macroeconomic stability.
Keywords
Deterministic Chaos, Fractal Analysis, Kolmogorov&ndash
Sinai Entropy, Long Memory, Permutation Entropy
Subjects
References
Anishchenko, V. S. et al. (2008). Testing chaotic dynamics via Lyapunov exponents. Physica D: Nonlinear Phenomena, 114(1-2), 1-2.
Ahmadi, M. (2021). Research on the Dynamics of Exchange Rate and Behavioral Structures in the Iranian Economy. University of Tehran. [In persian]
Abolhasani, A., Elmi, M., & Mansouri, N. (2023). The impact of financial and trade sanctions on the exchange rate in Iran: A fuzzy approach. Journal of Financial Economics, 17(2), 49-94. [In persian]
Atefimanesh, R. (2015). A review of exchange rate regime classification in OIC member countries and recommendations for Iran. Journal of Monetary and Fiscal Policies, 3(10), 32-57. [In persian]
Azari, S., & Fazeli, M. (2019). Estimating the pass-through of exchange rate to domestic prices in the Iranian economy. Iranian Economic Research Quarterly, 54(2), 45-68. [In persian]
Babazadeh, M., Elmi, S., Etebari, F., & Mahmoudzadeh, S. (2009). Chaotic behavior in the Iranian foreign exchange market using Lyapunov exponents and attractor dimension. Macroeconomics Research Journal, 37, 1-20. [In persian]
Babazadeh, M., Elmi, S., Etebari, F., & Mahmoudzadeh, S. (2008). Maximum Lyapunov exponent in the Iranian foreign exchange market: A chaos theory approach. Monetary and Banking Research, 1(2), 53-78. [In persian]
Bastanifar, I. (2016). Resilience in the monetary and exchange system and its structural requirements under economic threats. Afaq-e Amniat, 31, 5-28. [In persian]
Bask, M. (1996). Dimensions and Lyapunov exponents from exchange rate series. Chaos, Solitons & Fractals, 7(12), 2199-2214.
Central Bank of the Islamic Republic of Iran. (2012). Exchange rate report, 2011. Tehran: Central Bank of Iran. [In persian]
Clawson, P., & Sasanpour, C. (1987). Currency shock adjustment: Iran, 1951-1953. International Journal of Middle East Studies, 19, 1-22.
Datta, S. (2024). Entropy measures and exchange rate volatility: Evidence from emerging markets. Sustainable Computing: Informatics and Systems, 41, 101247.
Devaney, R. L. (2021). An Introduction to Chaotic Dynamical Systems (3rd. ed.). Chapman and Hall/CRC.
Gao, L., Chen, Y., & Huang, Z. (2023). Assessing chaotic dynamics in currency exchange markets using Lyapunov exponent and fractal dimension. Chaos, Solitons & Fractals, 174, 113054.
Gencay, R., & Dechert, W. D. (1992). Lyapunov exponents as a nonparametric diagnostic for stability analysis. Journal of Applied Econometrics, 7(S), S41-S60.
Guo, J., & Chen, S. (2021). Measuring nonlinear dependence and chaos in exchange rate markets. Physica A: Statistical Mechanics and its Applications, 567, 125634.
Hashemi, M., & Hari, M. S. (2014). Chaotic processes in the stock market using the BDS test and Lyapunov exponent. Journal of Financial Management and Investment, n.d., n.p. [In persian]
Heidari, H., & Aziznejad, S. (Eds.). (2021). Foreign Exchange Market and Exchange Rate Policies in Iran: Lessons from International Crises. Tehran: Iranian Parliament Research Center. [In persian]
Kantz, H., & Schreiber, T. (2003). Nonlinear Time Series Analysis (2nd. ed.). Cambridge University Press.
Kazemi, J., & Nikkhah, M. (2022). Analyzing exchange rate increases and their impact on selected macroeconomic variables in Iran. Iranian Economic Research Quarterly, 56(1), 34-56. [In persian]
Jafari, H., & Rezaei, A. (2023). The effect of real effective exchange rate and its uncertainties on value added of Iran’s industrial sector. Iranian Economic Studies Quarterly, 14(2), 78-101. [In persian]
Kuo, W., & Cho, K. (2021). Chaos and complexity in currency markets: An empirical study using entropy and Lyapunov exponents. Physica A, 570, 125877.
Lahmiri, S., & Serletis, A. (2024). Combined Lyapunov exponent and Kolmogorov-Sinai entropy in exchange rate dynamics. Chaos, Solitons & Fractals, 175, 113063. https://doi.org/10.1016/j.chaos.2024.113063
Lee, J., Park, S., & Kim, Y. (2020). Nonlinear and chaotic behavior of foreign exchange rates: An application of BDS and entropy tests. Physica A, 537, 122660.
Marzban, H., Javaheri, B., & Akbarian, R. (2005). A comparison of econometric, time-series, and neural network models in forecasting exchange rates. Quarterly Journal of Economic Research, 40(2), 35-60. [In persian]
Mahmoudi, R., & Salehi, F. (2021). Exchange rate fluctuations and their effects on selected macroeconomic variables in Iran. Iranian Macroeconomics Journal, 30(4), 89-112. [In persian]
Meng, F. et al. (2013). Analysis for global characteristics of Lyapunov exponents in exchange rate time series. Scientific Reports, 12, 13411.
Norouzi, H., Reshnovadi, Y., Firoozan-Sarneghi, T., & Beigi, Sh. (2019). Interactions between exchange rates and the Iranian stock market: A simultaneous equation system approach. Economic Modeling Research, 39(10), 20-56. [In persian]
Oman Adjeponng, E., Mensah, R., & Darko, F. (2023). Detecting nonlinearities and chaotic dynamics in foreign exchange markets: Evidence from multiple currency pairs. Physica A, 589, 126680.
Özkaya, A. (2022). Evidence of chaotic behavior in the Turkish lira exchange rates: A nonlinear dynamics approach. Physica A, 594, 127032.
Sadeghi, F. (2002). A review of chaos theory and its applications in economics. Iranian Economic Research Quarterly, 12, 29-50. [In persian]
Sadeghi, A., & Tayebi, S. K. (2018). The effects of international sanctions and other determinants on inflation in Iran (1981-2017). Iranian Economic Research, 74, 33-57. [In persian]
Salehi-Isfahani, D., & Pesaran, M. H. (2022). The Iranian Economy in the Twentieth Century: A Global Perspective. Cambridge: Cambridge University Press.
Shakeri, A. (2025). Economic Historiography of Iran over Six Decades (1960-2021). Tehran: Ney Publishing. [In persian]
Shaliari, F., Armen, S. A., & Salahmanesh, A. (2022). The effect of exchange rate uncertainty on inflation and interest rate volatility: The role of monetary and fiscal policy credibility. Iranian Journal of Applied Economic Studies, 11(43), 9-37. [In persian]