Author(s)

Jan Vrbik

Department of Mathematics and Statistics, Brock University, St. Catharines, Canada.

We discuss formulas and techniques for finding maximum-likelihood estimators of parameters of autoregressive (with particular emphasis on Markov and Yule) models, computing their asymptotic variance-covariance matrix and displaying the resulting confidence regions; Monte Carlo simulation is then used to establish the accuracy of the corresponding level of confidence. The results indicate that a direct application of the Central Limit Theorem yields errors too large to be acceptable; instead, we recommend using a technique based directly on the natural logarithm of the likelihood function, verifying its substantially higher accuracy. Our study is then extended to the case of estimating only a subset of a model’s parameters, when the remaining ones (called nuisance) are of no interest to us.

Markov, Yule and Autoregressive Models, Maximum Likelihood Function, Asymptotic Variance-Covariance Matrix, Confidence Intervals, Nuisance Parameters

Vrbik, J. (2023) Constructing Confidence Regions for Autoregressive-Model Parameters. Applied Mathematics, 14, 704-717. doi: 10.4236/am.2023.1410042.