Correlograms for non-stationary autoregressions

Analysis of economic time series often involves correlograms and partial correlograms as graphical descriptions of temporal dependence. Two methods are available for computing these statistics: one based on autocorrelations and the other on scaled autocovariances. For stationary time series the resulting plots are nearly identical. When it comes to economic time series that usually exhibit non-stationary features these methods can lead to very different results. This has two consequences: (i) incorrect inferences can be drawn when confusing these concepts; (ii) a better discrimination between stationary and non-stationarity appears when using autocorrelations rather than autocovariances which are commonly used in econometric software.