This research paper focuses on examining the behaviour of stock markets and investigating whether global stocks exhibit the property of long memory. Several methodologies, such as aggregated variance, rescaled-range analysis, and the periodogram, are employed to test this hypothesis. The criteria for determining the presence of long memory involve the point estimation of the Hurst exponent. Beyond point estimation, the return series and volatility series are further analysed using rolling samples to observe the dynamic nature of long memory over the studied period. Our findings suggest that market behaviour evolves over time, demonstrating that a single static Hurst exponent is insufficient to assess the overall efficiency of the market.