Hurst’s analysis of natural background microtremors at 10 stations in Yun-Li and Chia-Yi Counties, Taiwan, yields high values of H, ranging from 0.733 to 0.934. These values are found to be site-specific and stationary. Microtremors recorded in the foothills, on a hillside and at rock sites have higher H values than those on the alluvial plain, near the coast or at soil sites although they may very well be affected by the local environment and geology. Since low-frequency microtremors tend to be more persistent in time, we suggest that the high values of the Hurst exponent H may be causally correlated with the presence of low frequencies. This seems likely because Hurst exponents H > 0.5 mean a higher statistical persistence of a random signal.