A Time-Varying Cholesky GARCH Model for Dynamic Dependence Modeling

Articles in Press

Document Type : Original Article

Authors
Ferdous Mohammadi Basatini 1
Saeid Rezakhah 2
1 Department of Mathematics and Statistics, Shoushtar Branch, Islamic Azad University, Shoushtar, Iran.
2 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
10.22034/jirss.2026.2039785.1076
Abstract
In financial time series, dependencies can reflect the effects of different markets on each other, so evaluation of the instantaneous dependencies is of great importance in modelling multivariate financial time series. Maintaining positive-definiteness constraint of the time-varying covariance matrix is an important issue in multivariate models. Special attention is needed to maintain this constraint when the dimension of data is large. Cholesky GARCH model introduced based on Cholesky decomposition of the covariance matrix, inherently guarantees the positive-definiteness constraint of the time-varying covariance matrix. To describe instantaneous dependencies, we consider time-varying coefficients in Cholesky GARCH model. The regression coefficients are updated through a Gaussian random-walk. These coefficients are estimated using Kalman filter method based on the newest information as they arrive. The simulation and real data studies reveal the superior performance of the proposed time-varying Cholesky GARCH model compared to the previous models by capturing instantaneous dependencies.
Keywords
Cholesky decomposition
Dependencies
Gaussian random-walk
time-varying covariance matrix
Subjects
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Journal of the Iranian Statistical Society

Articles in Press, Accepted Manuscript
Available Online from 08 September 2026

  • Receive Date 29 August 2024
  • Revise Date 09 June 2026
  • Accept Date 25 July 2026