The Use of Minimization Solvers for Optimizing Time-Varying Autoregressive Models and Their Applications in Finance

Zhixuan Jia (), Wang Li, Yunlong Jiang and Xingshen Liu
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Zhixuan Jia: School of Information Management, Wuhan University, Wuhan 430072, China
Wang Li: School of Information Management, Wuhan University, Wuhan 430072, China
Yunlong Jiang: School of Information Management, Wuhan University, Wuhan 430072, China
Xingshen Liu: School of Information Management, Wuhan University, Wuhan 430072, China

Mathematics, 2025, vol. 13, issue 14, 1-21

Abstract: Time series data are fundamental for analyzing temporal dynamics and patterns, enabling researchers and practitioners to model, forecast, and support decision-making across a wide range of domains, such as finance, climate science, environmental studies, and signal processing. In the context of high-dimensional time series, the Vector Autoregressive model (VAR) is widely used, wherein each variable is modeled as a linear combination of lagged values of all variables in the system. However, the traditional VAR framework relies on the assumption of stationarity, which states that the autoregressive coefficients remain constant over time. Unfortunately, this assumption often fails in practice, especially in systems subject to structural breaks or evolving temporal dynamics. The Time-Varying Vector Autoregressive (TV-VAR) model has been developed to address this limitation, allowing model parameters to vary over time and thereby offering greater flexibility in capturing non-stationary behavior. In this study, we propose an enhanced modeling approach for the TV-VAR framework by incorporating minimization solvers in generalized additive models and one-sided kernel smoothing techniques. The effectiveness of the proposed methodology is assessed using simulations based on non-homogeneous Markov chains, accompanied by a detailed discussion of its advantages and limitations. Finally, we illustrate the practical utility of our approach using an application to real-world financial data.

Keywords: time-varying autoregressive model; generalized additive models; one-sided kernel smoothing; high-dimensional financial time series analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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