Limitations in timing precision due to single-pulse shape variability in millisecond pulsars

High-sensitivity radio-frequency observations of millisecond pulsars usually show stochastic, broadband, pulse-shape variations intrinsic to the pulsar emission process. These variations induce jitter noise in pulsar timing observations; understanding the properties of this noise is of particular importance for the effort to detect gravitational waves with pulsar timing arrays. We assess the short-term profile and timing stability of 22 millisecond pulsars that are part of the Parkes Pulsar Timing Array sample by examining intra-observation arrival time variability and single-pulse phenomenology. In 7 of the 22 pulsars, in the band centred at approximately 1400MHz, we find that the brightest observations are limited by intrinsic jitter. We find consistent results, either detections or upper limits, for jitter noise in other frequency bands. PSR J1909-3744 shows the lowest levels of jitter noise, which we estimate to contribute $\sim$10 ns root mean square error to the arrival times for hour-duration observations. Larger levels of jitter noise are found in pulsars with wider pulses and distributions of pulse intensities. The jitter noise in PSR J0437-4715 decorrelates over a bandwidth of $\sim$2 GHz. We show that the uncertainties associated with timing pulsar models can be improved by including physically motivated jitter uncertainties. Pulse-shape variations will limit the timing precision at future, more sensitive, telescopes; it is imperative to account for this noise when designing instrumentation and timing campaigns for these facilities.