Causality conditions and autocovariance calculations in PVAR models

Abstract

This paper studies the causality conditions and autocovariance calculations in periodic vector auto-regressions. A state-space representation is exploited to extract a simple, necessary and sufficient condition for periodic stationarity, under which the autocovariances can be expressed in a simple but tractable form. The proposed methods compute the autocovariances for distinct seasons separately, thereby facilitating efficient computation for models with a large period.

Keywords:

• Periodic VAR models
• Periodic stationarity
• Periodic autocovariances
• discrete-time periodic Lyapunov equation

Acknowledgements

The author expresses his most sincere thanks and grateful acknowledgement to the anonymous referee for his important corrections to some errors in an earlier version and his useful suggestions that have improved the form and the content of the paper. Also, the author is grateful to his supervisor, Professor M. Bentarzi, for his considerable help and contribution, and to his colleagues Dr H. Guerbyenne and Mr N. Kaciabdellah for their important help and encouragement.

Additional information

Notes on contributors

Abdelhakim Aknouche

Email: [email protected]