On linear prediction for stationary random fields with nonsymmetrical half-plane past

Abstract

An explicit autoregressive series representation for the best multi-step ahead linear predictor of stationary random fields with nonsymmetrical half-plane past (NSHP) is established. Necessary and sufficient condition for the mean square convergence of these series is given. Moreover, step recursive relations between the prediction coefficients for the infinite past predictor are provided, these relations are used to calculate explicitly the multi-step prediction coefficients. Some specific examples to validate the applicability of our relations are presented.

Keywords:

• Stationary random fields
• linear prediction
• multi-step prediction
• mean square convergence

MATHEMATICAL SUBJECT CLASSIFICATION:

• 60G60
• 60G25

Additional information

Funding

The authors thank the General Directorate of Scientific Research and Technological Development (DGRSDT/MESRS-Algeria) for their financial support.