We analyse the timing residuals for 50 pulsars observed using the Nanshan 25-m radio telescope at Urumqi Observatory by determining the Hurst parameter for each data set using the rescaled range method. These pulsars have been observed over a time span of 5–8 yr and have been selected to have timing residuals that resemble white noise rather than smooth curves. The results are compared with those for shuffled residual series. Despite the noise-like appearance, some timing residual series showed Hurst parameters that deviated significantly from the shuffled series. We conclude that Hurst parameter analysis is capable of detecting long-term memory in timing residuals.