Maximum-Likelihood Estimation Using the Zig-Zag Algorithm

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We analyze the properties of the Maximum Likelihood (ML) estimator when the underlying log-likelihood function is numerically maximized with the so-called zig-zag algorithm. By splitting the parameter vector into sub-vectors, the algorithm maximizes the log-likelihood function alternatingly with respect to one sub-vector while keeping the others constant. For situations when the algorithm is initialized with a consistent estimator and is iterated sufficiently often, we establish the asymptotic equivalence of the zig-zag estimator and the "infeasible"ML estimator being numerically approximated. This result gives guidance for practical implementations. We illustrate how to employ the algorithm in different estimation problems, such as in a vine copula model and a vector autoregressive moving average model. The accuracy of the estimator is illustrated through simulations. Finally, we demonstrate the usefulness of our results in an application, where the Bitcoin heating 2017 is analyzed by a dynamic conditional correlation model.

Details

Original languageEnglish
Pages (from-to)1346-1375
Number of pages30
JournalJournal of financial econometrics
Volume21 (2023)
Issue number4
Publication statusPublished - 1 Apr 2022
Peer-reviewedYes

External IDs

ORCID /0000-0002-8909-4861/work/149081751

Keywords

ASJC Scopus subject areas

Keywords

  • Bitcoin, C13, C50, dynamic conditional correlation, efficient estimation, Gauß-Seidel, iterative estimation, maximization by parts, vector autoregressive moving average, vine copula

Library keywords