Solar time series analysis is one of the most important topics in statistical astrophysics, which aims at revealing the complex dynamical behavior of long-term solar magnetic activity. In this work, several statistical analysis techniques are combined to study the long-term persistence and phase relationship of monthly filament activity between the low latitudes and the high latitudes during the time period from 1957 April to 2010 June. Based on these advanced analysis approaches, the following remarkable results are found: (1) solar filament activity at the low latitudes lags behind that at the high latitudes with a phase shift of 40 months, and the largest positive coefficient is found to be 0.35; (2) solar filament activity at both the low and the high latitudes exhibits a strong long-term persistence behavior, that is, their nonlinear dynamical behavior could not be regarded as stochastic phenomenon; (3) the relative phase relationships between the low latitudes and the high latitudes are not in phase for the studied periodic scales, but they are coherent in the periods of 10-14 years. To sum up, the analysis results could give more useful information on our understanding the solar and the stellar dynamo theory, and also provide some crucial roles of solar magnetic activity variations.