Spatial and Temporal Time Series Conversion - A Consistent Estimator of the Error Variance-Covariance Matrix. Abstract: We focus on the problem of time series conversion from low to high frequency satisfying the twofold temporal and spatial constraint. We offer a simple solution to variance-covariance matrix estimation of the error terms. Since the residuals of high frequency equations of the indicated indicator model are not observable, we inferred the characteristics of their stochastic process through both a specific hypothesis (VAR 1 process) and estimation of the related annual model. We derive a consistent estimator of the variance-covariance matrix and we prove that Di Fonzo's (1990) estimator based on this matrix is asymptotically equivalent to a GLS estimator.