Maximum Trimmed Likelihood Estimation for Discrete Multivariate Vasicek Processes

Thomas Fullerton (), Michael Pokojovy, Andrews T. Anum and Ebenezer Nkum
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Michael Pokojovy: Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA
Andrews T. Anum: Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, USA
Ebenezer Nkum: Cigna Healthcare, Nashville, TN 37228, USA

Economies, 2025, vol. 13, issue 3, 1-28

Abstract: The multivariate Vasicek model is commonly used to capture mean-reverting dynamics typical for short rates, asset price stochastic log-volatilities, etc. Reparametrizing the discretized problem as a VAR(1) model, the parameters are oftentimes estimated using the multivariate least squares (MLS) method, which can be susceptible to outliers. To account for potential model violations, a maximum trimmed likelihood estimation (MTLE) approach is utilized to derive a system of nonlinear estimating equations, and an iterative procedure is developed to solve the latter. In addition to robustness, our new technique allows for reliable recovery of the long-term mean, unlike existing methodologies. A set of simulation studies across multiple dimensions, sample sizes and robustness configurations are performed. MTLE outcomes are compared to those of multivariate least trimmed squares (MLTS), MLE and MLS. Empirical results suggest that MTLE not only maintains good relative efficiency for uncontaminated data but significantly improves overall estimation quality in the presence of data irregularities. Additionally, real data examples containing daily log-volatilities of six common assets (commodities and currencies) and US/Euro short rates are also analyzed. The results indicate that MTLE provides an attractive instrument for interest rate forecasting, stochastic volatility modeling, risk management and other applications requiring statistical robustness in complex economic and financial environments.

Keywords: econometric modeling; autoregressive models; times series analysis; maximum trimmed likelihood estimation; statistical robustness; outliers (search for similar items in EconPapers)
JEL-codes: E F I J O Q (search for similar items in EconPapers)
Date: 2025
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