The smooth spin-down of young pulsars is perturbed by two non-deterministic phenomenon, glitches, and timing noise. Although the timing noise provides insights into nuclear and plasma physics at extreme densities, it acts as a barrier to high-precision pulsar timing experiments. An improved methodology based on the Bayesian inference is developed to simultaneously model the stochastic and deterministic parameters for a sample of 85 high-|$\dot{E}$| radio pulsars observed for ∼10 yr with the 64-m Parkes radio telescope. Timing noise is known to be a red process and we develop a parametrization based on the red-noise amplitude (Ared) and spectral index (β). We measure the median Ared to be |$-10.4^{+1.8}_{-1.7}$| yr3/2 and β to be |$-5.2^{+3.0}_{-3.8}$| and show that the strength of timing noise scales proportionally to |$\nu ^{1}|\dot{\nu }|^{-0.6\pm 0.1}$|⁠, where ν is the spin frequency of the pulsar and |$\dot{\nu }$| is its spin-down rate. Finally, we measure significant braking indices for 19 pulsars and proper motions for 2 pulsars, and discuss the presence of periodic modulation in the arrival times of 5 pulsars.

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