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Vrbik, J. and Vrbik, P. (2013) Informal Introduction to Stochastic Processes with Maple. Springer, New York.
https://doi.org/10.1007/978-1-4614-4057-4

has been cited by the following article:

• TITLE: Constructing Confidence Regions for Autoregressive-Model Parameters

  AUTHORS: Jan Vrbik

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

  JOURNAL NAME: Applied Mathematics, Vol.14 No.10, October 31, 2023

  ABSTRACT: 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.