The long-term stability of pulsar time (PT) is susceptible to the influence of red noise within timing residuals. Based on the first release data from the International Pulsar Timing Array, we apply a generalized least-squares (GLS) solution based on the “Cholesky” method to process the red noise, thereby obtaining improved pulsar model parameters for timing residual forecasting. Through two distinct prediction schemes, we analyze the relative frequency deviation of the Terrestrial Time (TT) realisation based on PT (TT(PT)), compared to the TT provided by the Bureau International des Poids et Mesures. Results indicate that relative frequency deviations are significantly reduced following the GLS-processed red noise, with relative reductions ranging from 23% to 60% depending on the pulsar and forecasting scheme, effectively enhancing TT (PT) accuracy. Furthermore, PSR J1713+0747 exhibited no improvement after red-noise mitigation, as its long-term high-precision data and non-power-law features of its residuals biased the noise model. Research confirms that red noise processing is of significant value to constructing high-precision PT.