Evaluating exact VARMA likelihood and its gradient when data are incomplete

Authors:
Kristjan Jonasson;Sebastian E. Ferrando
Affiliations:
University of Iceland, Reykjavik, Iceland;Ryerson University
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2008

Citing 5
Cited 1

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Algorithm 808: ARfit—a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models

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Algorithm 878: Exact VARMA likelihood and its gradient for complete and incomplete data with Matlab

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Exact maximum likelihood estimation of structured or unit root multivariate time series models

Computational Statistics & Data Analysis

Algorithm 878: Exact VARMA likelihood and its gradient for complete and incomplete data with Matlab

ACM Transactions on Mathematical Software (TOMS)

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Abstract

A detailed description of an algorithm for the evaluation and differentiation of the likelihood function for VARMA processes in the general case of missing values is presented. The method is based on combining the Cholesky decomposition method for complete data VARMA evaluation and the Sherman-Morrison-Woodbury formula. Potential saving for pure VAR processes is discussed and formulae for the estimation of missing values and shocks are provided. A theorem on the determinant of a low rank update is proved. Matlab implementation of the algorithm is in a companion article.