Some prediction problems for stationary random fields with quarter-plane past Academic Article

abstract

• We study several nonstandard prediction problems where a number of observations are added to the quarter-plane past of a stationary random field. The goal is to provide informative and explicit prediction error variance formulas in terms of either the autoregressive or moving average parameters of the random fields. However, unlike the time series situation, the prediction error variances for random fields seem to be expressible only in terms of the moving average parameters, and attempts to express them formally in terms of the autoregressive parameters lead to a new and mysterious projection operator which captures the nature of the "edge-effects" encountered in the estimation of the spectral density function of stationary random fields. The approach leads to a number of technical issues and open problems. 2014.

authors

• Pourahmadi, Mohsen

published proceedings

• JOURNAL OF MULTIVARIATE ANALYSIS

author list (cited authors)

• Kohli, P., & Pourahmadi, M.

citation count

• 6

complete list of authors

• Kohli, P||Pourahmadi, M

publication date

• January 2014

publisher

• Elsevier  Publisher

published in

• Journal of Multivariate Analysis  Journal

keywords

• Edge-effects
• Projection Operator
• Random Field
• Spatial Prediction
• Unilateral Representation
• Wold Decomposition

Digital Object Identifier (DOI)

• 10.1016/j.jmva.2014.02.009

start page

• 112

end page

• 125

volume

• 127

issue

• C

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jmva.2014.02.009