Modelling and estimating relationships that combine time series and crosssectional
data is often discussed in the statistical literature but in these considerations sampling
errors are seldom taken into account. In the paper the application of the Rao-Yu model involving
both- autocorrelated random effects between areas and sampling errors-has been presented. On the
basis of this model the empirical best linear unbiased predictor (EBLUP) with time correlation has
been obtained. As an example the application of several income-related variables for the Polish
voivodships (regions) and the years 2003–2011 was used on the basis of the Polish Household
Budget Survey and selected explanatory variables obtained from Polish Local Data Bank. The
computations were performed using sae2 and sae packages for R-project environment and
WesVAR software. The precision of the direct estimates was obtained using Balanced Repeated
Replication (BRR) technique.
For most investigated cases, the proposed methods based on the Rao-Yu model yielded the
significant improvement of small area estimates due to substantial reduction of their relative
estimation errors as compared to the ordinary EBLUP technique. For some income variables
examined within the study very high values of time-related autocorrelation coefficient were
observed. These values were in some cases higher than 0.9, what can be – in our opinion – a good
illustration of income growth tendency observed in Poland in the period under consideration.