Separable approximations of space-time covariance matrices

Marc G. Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

119 Scopus citations


Statistical modeling of space-time data has often been based on separable covariance functions, that is, covariances that can be written as a product of a purely spatial covariance and a purely temporal covariance. The main reason is that the structure of separable covariances dramatically reduces the number of parameters in the covariance matrix and thus facilitates computational procedures for large space-time data sets. In this paper, we discuss separable approximations of nonseparable space-time covariance matrices. Specifically, we describe the nearest Kronecker product approximation, in the Frobenius norm, of a space-time covariance matrix. The algorithm is simple to implement and the solution preserves properties of the space-time covariance matrix, such as symmetry, positive definiteness, and other structures. The separable approximation allows for fast kriging of large space-time data sets. We present several illustrative examples based on an application to data of Irish wind speeds, showing that only small differences in prediction error arise while computational savings for large data sets can be obtained.

Original languageEnglish (US)
Pages (from-to)681-695
Number of pages15
Issue number7
StatePublished - Nov 2007
Externally publishedYes


  • Block Toeplitz matrix
  • Kriging
  • Kronecker product
  • Nonstationarity
  • Positive definiteness
  • Separable covariance
  • Space-time stochastic process
  • Stationarity

ASJC Scopus subject areas

  • Statistics and Probability
  • Ecological Modeling


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