The long-range correlations associated with the presence of persistence are investigated by applying the detrended fluctuation analysis (DFA) on three different proxies of long-term solar activity. The considered datasets are a sunspot number reconstruction (SNR04) obtained from the atmospheric activity of the cosmogenic isotope 14C derived from tree rings, a total solar irradiance reconstruction (TSIR12) obtained from several 10Be ice core records from Greenland and Antarctica in combination with the global record of 14C in tree rings and a new multi-proxy sunspot number reconstruction (SNR18), also derived from 10Be datasets and the global 14C production series. The DFA scaling exponents found for the three time series are similar (lying in the range between 0.70 and 0.77) and the scaling ranges are comparable. These results indicate the presence of long-range correlations with persistence, in substantial agreement with the findings of previous studies carried out on other solar activity indices and proxies.