Hydrologic persistence is a unique property that explains the temporal clustering of extreme events such as floods and droughts. It influences the inter-arrival times of these extreme events and helps in understanding the mechanism of their return periods. In this work, the influence of rainfall amount and changing patterns of dry and wet spells on persistence of their joint behaviour is investigated at multiple time scales through estimation of Hurst Exponent (H) using Detrended Fluctuation Analysis (DFA) and Detrended Cross-Correlation Analysis (DCCA) at MOPEX (Model Parameter Estimation Project) catchments in United States. The effect of catchment size on the persistence of streamflow at multiple temporal scales is also analyzed. The results of the analyses suggest that the state of persistence of joint behavior of streamflow and rainfall is neither affected by rainfall amount nor by the changing patterns of the dry and wet spells. However, the state of persistence of rainfall is affected by the patterns of dry and wet spells of observed rainfall. The results also suggest that catchment area has a significant effect on the persistence of rainfall as there exists a statistically significant correlation between catchment area and H estimated at multiple time scales. Overall, the study finds that catchment acts as a filter that transforms rainfall with low or no persistence to streamflow with higher persistence manifested by different catchment characteristics at multiple spatio-temporal scales.