Research on cointegration for vector fractional integration time series

Some properties of cointegration for vector fractional integration time series were presented,and a necessary condition for the linear cointegration was given.Then,the concept of integer-order generalized cointegration was extended to that of fraction-order.Based on the definition of generalized fractional cointegration,a sufficient condition for the existence of nonlinear cointegration for vector fractional integration time series was obtained,and a specific nonlinear function form was derived.Combining with R/S analysis,a practical algorithm for judgment of the nonlinear cointegration was worked out.