2013MNRAS.428.1147V

Although it is widely understood that pulsar timing observations generally contain time-correlated stochastic signals (TCSSs; red timing noise is of this type), most data analysis techniques that have been developed make an assumption that the stochastic uncertainties in the data are uncorrelated, i.e. `white'. Recent work has pointed out that this can introduce severe bias in the determination of timing-model parameters and that better analysis methods should be used. This paper presents a detailed investigation of timing-model fitting in the presence of TCSSs and gives closed expressions for the post-fit signals in the data. This results in a Bayesian technique to obtain timing-model parameter estimates in the presence of TCSSs, as well as computationally more efficient expressions of their marginalized posterior distribution. A new method to analyse hundreds of mock data set realizations simultaneously without significant computational overhead is presented, as well as a statistically rigorous method to check the internal consistency of the results. As a by-product of the analysis, closed expressions of the rms introduced by a stochastic background of gravitational waves in timing residuals are obtained, valid for regularly sampled data. Using T as the length of the data set and hc(1yr- 1) as the characteristic strain, this is σ_GWB^2 = h_c(1 yr^-1)^2 (9 \root 3 2π^4Γ(-10/3)/ 8008)  yr^-4/3 T^10/3.