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Power load fluctuation is generally agreed to be a non-stationary stochastic process. The Fractional Brownian Motion (FBM) model is proposed to forecast a non-stationary time series with high accuracy. Computation of the Hurst exponent (H) for the power load data series using the Rescaled Range Analysis (R/S) in this study. This method is used to verify the Long-Range Dependent (LRD) characteristics of non-stationary power load data. For the real power load, however, H exponent takes on the self-similarity characteristics in a certain finite range of intervals, the global self-similarity is very rare to exist. The H exponent of the self-similarity usually has more than one value. We generalize multifractional H (t) to replace constant H. To improve the forecasting accuracy, the H (t) is optimized by the Quantum-Behaved Particle Swarm Optimization (QPSO). Once the optimal H (t) is obtained, then the optimal and parameters in the multi-Fractional Brownian Motion (mFBM) model can be deduced to forecast next power load data series with a higher accuracy. • Fractional Brownian Motion (FBM)as Stochastic model forecasts a power load series. • The parameters of the FBM are estimated by R/S and MSE methods. • The parameters of the FBM are optimized by PSO and QPSO. • The prediction errors of RNN,FBM,PSO + FBM,QPSO + FBM were analyzed by using box-plot and norm-plot. [ABSTRACT FROM AUTHOR]