Data span and frequency coverage requirements for robust detection and inference in pulsar timing arrays

Pulsar timing arrays (PTAs) are approaching the level of sensitivity required to make a 5-sigma detection of the nanohertz stochastic gravitational-wave background (GWB). Thus, it is now crucial to develop a comprehensive understanding of our data and of the outcomes of our analysis pipelines. It is also essential to understand a counterintuitive feature revealed in the recent results from the European Pulsar Timing Array (EPTA) second data release (DR2). When restricting the dataset to its ultimate similar to 10.3 years (DR2new), the inferred GWB significance increases from less than or similar to 2 sigma for the full 25-year dataset (DR2full), to greater than or similar to 3.5 sigma for DR2new. In this work, we investigate whether this behaviour reflects an anomaly in the data or whether it is a possible outcome of the analysis pipeline. Using realistic DR2-like simulations, we generated multiple realisations with varying observation time spans and analysed their impact on GWB evidence and parameter estimations. We quantified the evidence using the signal-to-noise ratio (S/N) of a common process with Hellings-Downs spatial correlations (HD S/N). We find that the first similar to 10 years of DR2 contribute little to the GWB evidence due to the limited bandwidth of the observation frequency, leading to a significant overlap between the DR2full and DR2new HD S/N distributions. As a consequence, random noise fluctuations result in DR2new producing a higher GWB significance than DR2full in similar to 15% of the cases and 5% of the realisations are compatible with the HD S/N of the real DR2full and DR2new. This suggests that the picture observed in the data, while unlikely, remains consistent with a similar to 2 sigma outcome due to noise fluctuations. We also find that regardless of the significance, the DR2new simulated data yielded biased GWB parameter estimates, primarily due to spectral leakage effects that are disregarded in the analysis and tend to flatten the inferred power-law spectrum. Including leakage in the model returns unbiased parameter estimates, demonstrating that DR2new is reliable when the signal is appropriately modelled. Furthermore, we show that combining EPTA DR2full data with complementary long-baseline observations from NANOGrav and PPTA and with low-frequency observations from LOFAR and NenuFAR significantly bolsters the GWB evidence, along with improved precision and accuracy in the parameter estimation. This outcome supports the case of integrating DR2full within the IPTA framework. Finally, we explored the impact of the observation time span on parameter estimations in greater detail, focusing on long-baseline (25 yr) and short-baseline (5 yr) datasets. We find that short-baseline datasets tend to introduce significant bias towards high amplitudes in the estimation of GWB parameters, while the short time span makes them very ineffective at constraining the GWB slope.