Based on the tick-by-tick price changes of the companies from the U.S. and from the German stock markets over the period 1998--99 we reanalyse several characteristics established by the Boston Group for the U.S. market in the period 1994--95, which serves to verify their space and time-translational invariance. By increasing the time scales, in the region covered by the data, we find a significantly more accelerated departure from the power-law (\alpha \approx 3) asymptotic behaviour of the distribution of returns towards a Gaussian, both for the U.S. as well as for the German stock markets. In the latter case the crossover is even faster. Consistently, the corresponding autocorrelation functions of returns and of the time averaged volatility also indicate a faster loss of memory with increasing time. This route towards efficiency, as seen in a fixed time scale, may reflect a systematic increase of the quality of information processing when going from past to present.

PACS numbers: 89.20.--a, 89.65.Gh, 89.75.--k