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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. [ABSTRACT FROM AUTHOR]