Evaluating exact VARMA likelihood and its gradient when data are incomplete

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Evaluating exact VARMA likelihood and its gradient when data are incomplete

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 35 , Issue 1 (July 2008) table of contents

Article No. 5

Year of Publication: 2008

ISSN:0098-3500

Authors

Kristjan Jonasson	University of Iceland, Reykjavik, Iceland
Sebastian E. Ferrando	Ryerson University

Publisher

ACM New York, NY, USA

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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.

REFERENCES

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