Journal of Econometric Modelling

Journal of Econometric Modelling

Analysis of Lead–Lag Structure in the Iranian Stock Market: Path Signature and Lévy Model

Document Type : Original Article

Authors
Saeed Sadrzadeh Moghadam 1
Kambiz Hojabr Kiani 2
1 Ph.D. Student, Department of Economic, Faculty of Management and Economics, Islamic Azad University, Science and Research Branch
2 Prof. Department of Economic, Faculty of Economics, Shahid Beheshti University
10.22075/jem.2025.38489.2026
Abstract
This study proposes a novel framework for identifying and exploiting lead–lag relationships among stocks in the Iranian capital market. Leveraging the theory of path signature and Lévy area computation, dynamic lead–lag matrices were constructed over rolling time windows. Subsequently, Hermitian clustering was employed to uncover the evolving leader–follower structure within the market. Based on this structure, three portfolio strategies were developed: a global leader–follower portfolio (GP), a cluster-based portfolio (CP), and an aggregated cluster portfolio (GCP). The strategies were tested on daily price data of selected stocks from major industries over a multi-year horizon. Empirical results reveal that the GCP strategy achieved an annual return of 6% with a Sharpe ratio of 0.33, outperforming traditional methods such as Granger causality and CP. Notably, the lagged cross-correlation (CCF) approach, despite its simplicity, yielded a strong annual return of 11.5% and a Sharpe ratio of 0.61, surpassing all classical models. Furthermore, an industry-weighted portfolio based on aggregated inter-industry lead–lag flows outperformed all strategies, with an impressive annual return of 31.3% and a Sharpe ratio of 1.51. These findings indicate that temporal and cross-symbol dependencies hold valuable predictive information for portfolio design and market timing. Moreover, the integration of intra-industry and inter-industry analyses provides additional insight into the structural flow of information within the market. The proposed framework offers a robust foundation for dynamic portfolio optimization and highlights the value of modern mathematical tools in financial modeling.
Keywords
Lead Lag Structure
Path Signature
Levy Area Model
Hermitian Clustering
Granger Causality

Aghababayi, R. & Rezaei, A. (2019). Analyzing lead–lag relationships between industry returns in Tehran Stock Exchange: A VAR model approach. Behavioral Financial Studies, 3(2), 55–74. [In Persian]

Bartbour, M. Emamvirdi, G. Mahmoudzadeh, M. & Saltina, P. (2024). Analyzing the interaction between leading stocks and exchange rate shocks using network analysis and VAR-GARCH: Evidence from the Tehran Stock Exchange. Iranian Journal of Economic Studies, 13(1), 97–122. [In Persian]

Boudt, K. Cornelissen, J. & Laurent, S. (2017). Multivariate lead–lag relationships: A copula approach. Journal of Banking & Finance, 80, 100-114.

Box, G. E. & Jenkins, G. M. (1976). Time series analysis: Forecasting and control. Holden-Day.

Chordia, T. Roll, R. & Subrahmanyam, A. (2005). Evidence on the speed of convergence to market efficiency. Journal of Financial Economics, 76(2), 271–292.

Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339-350.

Friz, P. & Victoir, N. (2010). Multidimensional stochastic processes as rough paths: Theory and applications. Cambridge University Press.

Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.

Hong, H. & Stein, J. C. (1999). A unified theory of underreaction, momentum trading, and overreaction in asset markets. The Journal of Finance, 54(6), 2143–2184.

Jegadeesh, N. & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65–91.

Lo, A. W. & MacKinlay, A. C. (1990). An econometric analysis of nonsynchronous trading. Journal of Econometrics, 45(1-2), 181-211.

Lo, A. W. & MacKinlay, A. C. (1990). When are contrarian profits due to stock market overreaction? Review of Financial Studies, 3(2), 175–205.

Lyons, T. (2014). Rough paths, signatures and the modelling of functions on streams. Proceedings of the International Congress of Mathematicians.

Malliaros, F. D. & Vazirgiannis, M. (2013). Clustering and community detection in directed networks: A survey. Physics Reports, 533(4), 95-142.

Nourbakhsh, A. Taheri, M. & Saeedi, F. (2021). Examining lead–lag relationships between selected industry indices of Tehran Stock Exchange using Granger causality test. Financial Research Journal, 23(93), 67–88. [In Persian]

Taleblou, B. Kaviani, S. & Mousavi, M. (2022). Identifying leading stocks in Tehran Stock Exchange using complex networks and graph analysis. Quarterly Journal of Behavioral Finance, 5(2), 43–62. [In Persian]

Taleblou, R. and Mohajeri, P. (2022). Connectedness and Risk Spillovers in Iranian Stock Market: Using TVP-VAR in a Sectoral Analysis. Journal of Econometric Modelling, 7(3), 95-125. [In Persian]

Aghababayi, R. & Rezaei, A. (2019). Analyzing lead–lag relationships between industry returns in Tehran Stock Exchange: A VAR model approach. Behavioral Financial Studies, 3(2), 55–74. [In Persian]
Bartbour, M. Emamvirdi, G. Mahmoudzadeh, M. & Saltina, P. (2024). Analyzing the interaction between leading stocks and exchange rate shocks using network analysis and VAR-GARCH: Evidence from the Tehran Stock Exchange. Iranian Journal of Economic Studies, 13(1), 97–122. [In Persian]
Boudt, K. Cornelissen, J. & Laurent, S. (2017). Multivariate lead–lag relationships: A copula approach. Journal of Banking & Finance, 80, 100-114.
Box, G. E. & Jenkins, G. M. (1976). Time series analysis: Forecasting and control. Holden-Day.
Chordia, T. Roll, R. & Subrahmanyam, A. (2005). Evidence on the speed of convergence to market efficiency. Journal of Financial Economics, 76(2), 271–292.
Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business & Economic Statistics, 20(3), 339-350.
Friz, P. & Victoir, N. (2010). Multidimensional stochastic processes as rough paths: Theory and applications. Cambridge University Press.
Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.
Hong, H. & Stein, J. C. (1999). A unified theory of underreaction, momentum trading, and overreaction in asset markets. The Journal of Finance, 54(6), 2143–2184.
Jegadeesh, N. & Titman, S. (1993). Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48(1), 65–91.
Lo, A. W. & MacKinlay, A. C. (1990). An econometric analysis of nonsynchronous trading. Journal of Econometrics, 45(1-2), 181-211.
Lo, A. W. & MacKinlay, A. C. (1990). When are contrarian profits due to stock market overreaction? Review of Financial Studies, 3(2), 175–205.
Lyons, T. (2014). Rough paths, signatures and the modelling of functions on streams. Proceedings of the International Congress of Mathematicians.
Malliaros, F. D. & Vazirgiannis, M. (2013). Clustering and community detection in directed networks: A survey. Physics Reports, 533(4), 95-142.
Nourbakhsh, A. Taheri, M. & Saeedi, F. (2021). Examining lead–lag relationships between selected industry indices of Tehran Stock Exchange using Granger causality test. Financial Research Journal, 23(93), 67–88. [In Persian]
Taleblou, B. Kaviani, S. & Mousavi, M. (2022). Identifying leading stocks in Tehran Stock Exchange using complex networks and graph analysis. Quarterly Journal of Behavioral Finance, 5(2), 43–62. [In Persian]
Taleblou, R. and Mohajeri, P. (2022). Connectedness and Risk Spillovers in Iranian Stock Market: Using TVP-VAR in a Sectoral Analysis. Journal of Econometric Modelling, 7(3), 95-125. [In Persian]