Abstract: Runs of a stationary stochastic sequence follow a second-order homogeneous linear difference equation, in which, the difference equation of an independent series possesses a two fold characteristic root in terms of state generation average probabilities. The constants in the general solution can be determined by using a prior condition. Likewise, the difference equation of a dependent series has two distinct characteristic roots and the constants need to be derived from sampling data. The applicability of this method has been verified by using the drought series and the hygologic series.