Fractional Differencing
将自回归积分滑动平均模型推广到允许差分阶数为分数，定义了分数差分算子，该模型能刻画时间序列的长期持久性和反持久性，在经济学和水文学中有应用。
The family of autoregressive integrated moving-average processes, widely used in time series analysis, is generalized by permitting the degree of differencing to take fractional values. The fractional differencing operator is defined as an infinite binomial series expansion in powers of the backward-shift operator. Fractionally differenced processes exhibit long-term persistence and antipersistence; the dependence between observations a long time span apart decays much more slowly with time span than is the case with the more commonly studied time series models. Long-term persistent processes have applications in economics and hydrology; compared to existing models of long-term persistence, the family of models introduced here offers much greater flexibility in the simultaneous modelling of the short-term and long-term behaviour of a time series.