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Long memory is important in financial modeling.A stationary sequence admitslong memory if its auto-covariance sequence is absolutely summable.If the second moment of a stationary sequence is unbounded,such a characterizationis invalid because of the absence of auto-covariance sequence.We detect the long memory behavior of a stationary sequence by the finiteness of excess entropy,which can be used to stationary sequence of unbounded variance.Its validity is demonstrated by some typical examples.(This is a joint work with Y.Ding,et al.)