With Rossi X-ray Timing Explorer (RXTE) data, we systematically study the cross-correlation and time lag in all spectral states of black hole X-ray binary (BHXB) XTE J1859+226 in detail during its entire 1999-2000 outburst that lasted for 166 days. Anti-correlations and positive correlations and their respective soft and hard X-ray lags are only detected in the first 100 days of the outburst when the luminosity is high. This suggests that the cross-correlations may be related to high luminosity. Positive correlations are detected in every state of XTE J1859+226, viz., hard state, hard-intermediate state (HIMS), soft-intermediate state (SIMS) and soft state. However, anti-correlations are only detected in HIMS and SIMS, anti-correlated hard lags are only detected in SIMS, while anti-correlated soft lags are detected in both HIMS and SIMS. Moreover, the ratio of the observations with anti-correlated soft lags to hard lags detected in XTE J1859+226 is significantly different from that in neutron star low-mass X-ray binaries (NS LMXBs). So far, anti-correlations are never detected in the soft state of BHXBs but detected in every branch or state of NS LMXBs. This may be due to the origin of soft seed photons in BHXBs is confined to the accretion disk and, for NS LMXBs, from both accretion disk and the surface of the NS. We notice that the timescale of anti-correlated time lags detected in XTE J1859+226 is similar with that of other BHXBs and NS LMXBs. We suggest that anti-correlated soft lag detected in BHXB may result from fluctuation in the accretion disk as well as NS LMXB.
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