Variance of the Sample Space-time Autocorrelation Function

SUMMARY An important part of the diagnostic checking of space-time autoregressive moving average (STARMA) models is testing the temporal independence of the residuals. In the context of the three-stage modelling procedure,. such a test is based on the sample space-time autocorrelation function. This paper developes approximate variances of the sample space-time autocorrelation function when the underlying process is white noise, which are needed to test significance of the observed autocorrelations.