By establishing the Markov model for a long-range correlated time series (LRCS) and analysing its evolutionary characteristics, this paper defines a physical effective correlation length (ECL) T, which reflects the predictability of the LRCS. It also finds that the ECL has a better power law relation with the long-range correlated exponent γ of the LRCS: T = Kexp(-γ/0.3) + Y, (0 〈 γ〈 1) the predictability of the LRCS decays exponentially with the increase of γ It is then applied to a daily maximum temperature series (DMTS) recorded at 740 stations in China between the years 1960-2005 and calculates the ECL of the DMTS. The results show the remarkable regional distributive feature that the ECL is about 10-14 days in west, northwest and northern China, and about 5-10 days in east, southeast and southern China. Namely, the predictability of the DMTS is higher in central-west China than in east and southeast China. In addition, the ECL is reduced by 1-8 days in most areas of China after subtracting the seasonal oscillation signal of the DMTS from its original DMTS; however, it is only slightly altered when the decadal linear trend is removed from the original DMTS. Therefore, it is shown that seasonal oscillation is a significant component of daily maximum temperature evolution and may provide a basis for predicting daily maximum temperatures. Seasonal oscillation is also significant for guiding general weather predictions, as well as seasonal weather predictions.