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We consider the Adler $D$-function, which is defined in the spacelike region,and the $e^+e^-$ annihilation ratio smeared, according to the Poggio, Quinn,and Weinberg method, which is determined for timelike argument. We show thatthe method of the nonperturbative $a$-expansion allows one to describe theseEuclidean and Minkowskian characteristics of the process of $e^+e^-$annihilation down to the lowest energy scales.Comment: 11 pages, 4 eps figures, revte

Timelike and spacelike QCD characteristics of the