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A nanohertz-frequency stochastic gravitational-wave background canpotentially be detected through the precise timing of an array of millisecondpulsars. This background produces low-frequency noise in the pulse arrivaltimes that would have a characteristic spectrum common to all pulsars and awell-defined spatial correlation. Recently the North American NanohertzObservatory for Gravitational Waves collaboration (NANOGrav) found evidence forthe common-spectrum component in their 12.5-year data set. Here we report on asearch for the background using the second data release of the Parkes PulsarTiming Array. If we are forced to choose between the two NANOGrav models$\unicode{x2014}$ one with a common-spectrum process and one without$\unicode{x2014}$ we find strong support for the common-spectrum process.However, in this paper, we consider the possibility that the analysis suffersfrom model misspecification. In particular, we present simulated data sets thatcontain noise with distinctive spectra but show strong evidence for acommon-spectrum process under the standard assumptions. The Parkes data show nosignificant evidence for, or against, the spatially correlated Hellings-Downssignature of the gravitational-wave background. Assuming we did observe theprocess underlying the spatially uncorrelated component of the background, weinfer its amplitude to be $A = 2.2^{+0.4}_{-0.3} \times 10^{-15}$ in units ofgravitational-wave strain at a frequency of $1\, \text{yr}^{-1}$. Extensionsand combinations of existing and new data sets will improve the prospects ofidentifying spatial correlations that are necessary to claim a detection of thegravitational-wave background.

On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the Parkes Pulsar Timing Array