The paper applies the Lo and MacKinlay (1988) and Cochrane (1988) variance-ratio test to the data sample used by Nelson and Plosser (1982), who studies the stationarity properties of 14 macroeconomic variables. The results of our empirical tests indicate that the macroeconomic time series have significant random walk components, with the exception of unemployment, real wages, real per capita GNP and industrial production. These results generally agree with those reported earlier by Nelson and Plosser who found that 13 out of 14 macroeconomic variables followed random walk and with Cochrane who, more recently, found that GNP had a small random walk component. The contribution of this paper lies in its use of a very recent methodology to estimate the magnitude of the random walk component of certain macroeconomic time series.