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We report the detections of the anti-correlated soft and hard X-rays, and thetime lags of $\sim$ hecto-second from the neutron star low-mass X-ray binaryCyg X-2, a well-known Z-type luminous source. Both the anti-correlation and thepositive correlation were detected during the low-intensity states, while onlythe latter showed up during high-intensity states. Comparing with the lowerpart of normal branch and flaring branch, more observations located on thehorizontal and the upper normal branches are accompanied with theanti-correlation, implying the occurrence of the anti-correlation undercircumstance of a low mass accretion rate. So far the anti-correlated hard lagof thousand-second timescale are only reported from the Galactic black holecandidates in their hard states. Here we provide the first evidence that asimilar feature can also establish in a neutron-star system like Cyg X-2.Finally, the possible origins of the observed time lags are discussed under thecurrent LMXB models.

Evolution of cross-correlation and time lag of Cyg X-2 along the branches