Predictability: Beginning from the information entropy

We have established the Markov model for long range correlated time series (LRCS), by analyzing their evolutionary characteristics, then defined a physical effective correlation length (ECL) of the LRCS, which reflects the predictability of the LRCS, and find that the ECL has a better power law relation with the long range correlated exponent (LRCE) of the LRCS. We apply the power law relation between ECL and LRCE to the daily maximum temperature series (DMTS) at 740 stations in China for the period 1960-2005, calculate the ECL of the DMTS, and the results show the remarkable regional distributive features 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.