Evaluating exact VARMA likelihood and its gradient when data are incomplete

Kristjan Jonasson; Sebastian E. Ferrando

doi:10.1145/1377603.1377608

Evaluating exact VARMA likelihood and its gradient when data are incomplete

Kristjan Jonasson^*, Sebastian E. Ferrando

^*Corresponding author for this work

Faculty of Industrial Engineering, Mechanical Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Journal	ACM Transactions on Mathematical Software
Volume	35
Issue number	1
DOIs	https://doi.org/10.1145/1377603.1377608
Publication status	Published - 1 Jul 2008

Other keywords

ARMA
Determinant of low rank update
Exact likelihood function
Incomplete data
Matrix derivative
Matrix differentiation
Missing values
VARMA
Vector autoregressive moving average model

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10.1145/1377603.1377608

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AB - 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.

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KW - Determinant of low rank update

KW - Exact likelihood function

KW - Incomplete data

KW - Matrix derivative

KW - Matrix differentiation

KW - Missing values

KW - VARMA

KW - Vector autoregressive moving average model

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JO - ACM Transactions on Mathematical Software

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Evaluating exact VARMA likelihood and its gradient when data are incomplete

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