The article explores a new method for analyzing time series data that have long memory, which is common in fields like telecommunications and finance. Instead of assuming the data is stationary, the researchers allow for the long-memory parameter to change over time. They use a semi-parametric approach to estimate this changing parameter without fitting a specific model to the data. The researchers show that their method is reliable and can accurately estimate the time-varying parameter in a Gaussian context. Both simulations and real data examples support their findings.