Computational Maximum Likelihood Estimation of Nonlinear Time Series Regression Models with Correlated ARMA Errors
Faculty Mentor
Dr. Divine Wanduku
Location
Russell Union Ballroom
If Other was choses above, please indicate your topic area here:
Statistics
Type of Research
On-going
Session Format
Poster Presentation
College
College of Science & Mathematics
Department
Department of Mathematical Sciences
Abstract
Nonlinear time series regression models arising from dynamic systems frequently violate the assumption of independent errors. Serial dependence in the disturbance process, if ignored, leads to inefficient estimation, biased inference, and reduced predictive accuracy. This study develops a computational framework for nonlinear time series regression with correlated ARMA errors, motivated by an SIS compartmental epidemic model in which individuals transition between susceptible and infectious states.
The nonlinear infectious-state equation is fitted to time-indexed data under three competing error structures: AR(1), Random Walk–MA(1) (RW–MA(1)), and AR(1)–MA(1). Parameter estimation is performed using maximum likelihood and nonlinear least squares, implemented through a fully iterative Newton–Raphson algorithm. Recursive expressions for the score vector and Hessian enable simultaneous estimation of regression and dependence parameters. To enhance stability and predictive performance, LASSO-based regularization is incorporated within the optimization framework.
Simulation studies and empirical comparisons demonstrate that accounting for richer error dynamics significantly improves model performance. Evaluation using AIC, mean squared error (MSE), and mean absolute error (MAE) consistently shows that AR(1) error structures outperform the AR(1)–MA(1) and RW–MA(1) specification.
These results highlight the importance of structured error modeling in nonlinear time series regression and demonstrate the role of computational likelihood methods in advancing modern statistical and data science applications for dynamic systems.
Program Description
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Start Date
4-23-2026 2:00 PM
End Date
4-23-2026 4:00 PM
Recommended Citation
Olofin, Daniel O., "Computational Maximum Likelihood Estimation of Nonlinear Time Series Regression Models with Correlated ARMA Errors" (2026). GS4 Student Scholars Symposium. 174.
https://digitalcommons.georgiasouthern.edu/research_symposium/2026/2026/174
Computational Maximum Likelihood Estimation of Nonlinear Time Series Regression Models with Correlated ARMA Errors
Russell Union Ballroom
Nonlinear time series regression models arising from dynamic systems frequently violate the assumption of independent errors. Serial dependence in the disturbance process, if ignored, leads to inefficient estimation, biased inference, and reduced predictive accuracy. This study develops a computational framework for nonlinear time series regression with correlated ARMA errors, motivated by an SIS compartmental epidemic model in which individuals transition between susceptible and infectious states.
The nonlinear infectious-state equation is fitted to time-indexed data under three competing error structures: AR(1), Random Walk–MA(1) (RW–MA(1)), and AR(1)–MA(1). Parameter estimation is performed using maximum likelihood and nonlinear least squares, implemented through a fully iterative Newton–Raphson algorithm. Recursive expressions for the score vector and Hessian enable simultaneous estimation of regression and dependence parameters. To enhance stability and predictive performance, LASSO-based regularization is incorporated within the optimization framework.
Simulation studies and empirical comparisons demonstrate that accounting for richer error dynamics significantly improves model performance. Evaluation using AIC, mean squared error (MSE), and mean absolute error (MAE) consistently shows that AR(1) error structures outperform the AR(1)–MA(1) and RW–MA(1) specification.
These results highlight the importance of structured error modeling in nonlinear time series regression and demonstrate the role of computational likelihood methods in advancing modern statistical and data science applications for dynamic systems.
