Using all the observations from Rossi X-ray Timing Explorer for Z source GX 349+2, we systematically carry out cross-correlation analysis between its soft and hard X-ray light curves. During the observations from January 9 to January 29, 1998, GX 349+2 traced out the most extensive Z track on its hardness-intensity diagram, making a comprehensive study of cross-correlation on the track. The positive correlations and positively correlated time lags are detected throughout the Z track. Outside the Z track, anti-correlations and anti-correlated time lags are found, but the anti-correlated time lags are much longer than the positively correlated time lags, which might indicate different mechanisms for producing the two types of time lags. We argue that neither the short-term time lag models nor the truncated accretion disk model can account for the long-term time lags in neutron star low mass X-ray binaries (NS-LMXBs). We suggest that the extended accretion disk corona model could be an alternative model to explain the long-term time lags detected in NS-LMXBs.