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Pulse-to-pulse profile shape variations introduce correlations in pulsartimes of arrival (TOAs) across radio frequency measured at the sameobservational epoch. This leads to a broadband noise in excess of radiometernoise, which is termed pulse jitter noise. The presence of jitter noise limitsthe achievable timing precision and decreases the sensitivity of pulsar-timingdata sets to signals of interest such as nanohertz-frequency gravitationalwaves. Current white noise models used in pulsar timing analyses attempt toaccount for this, assuming complete correlation of uncertainties through thearrival times collected in a unique observation and no frequency dependence ofjitter (which corresponds to a rank-one covariance matrix). However, previousstudies show that the brightest millisecond pulsar at decimetre wavelengths,PSR J0437$-$4715, shows decorrelation and frequency dependence of jitter noise.Here we present a detailed study of the decorrelation of jitter noise in PSRJ0437$-$4715 and implement a new technique to model it. We show that the rateof decorrelation due to jitter can be expressed as a power-law in frequency. Weanalyse the covariance matrix associated with the jitter noise process and findthat a higher-rank-approximation is essential to account for the decorrelationand to account for frequency dependence of jitter noise. We show that the useof this novel method significantly improves the estimation of other chromaticnoise parameters such as dispersion measure variations. However, we find nosignificant improvement in errors and estimation of other timing modelparameters suggesting that current methods are not biased for other parameters,for this pulsar due to this misspecification. We show that pulse energyvariations show a similar decorrelation to the jitter noise, indicating acommon origin for both observables.

An insight into chromatic behaviour of jitter in pulsars and its modelling: A case study of PSR J0437$-$4715