A possible precursor for the detection of nanohertz gravitational waves or unmodeled pulsar noise?
Signals and noise in Pulsar Timing Arrays
Pulsar timing arrays (PTA) are experiments that perform monitoring of pulse arrival times from an ensemble of galactic millisecond pulsars, in order to search for the stochastic gravitationalwave background from supermassive binary black holes. One of the most exciting features of pulsar timing arrays is that most sources of noise are environmental, not just instrumental. This allows studying pulsar magnetospheres, interstellar medium, and more.
This is a short note about noise and signals in PTA.
Useful dimensional relations and acronyms
 PSD  power spectral density. Units:
 PTA  pulsar timing arrays
 ToA  pulse times of arrival
 DM  dispersion measure
Model for signals and noise
Data is modeled using a multivariate Gaussian likelihood function, which describes a probability distribution for the data (timing residuals), given the parameters of signals and noise. Each dimension of a multivariate likelihood distribution is related to the observation time.
There are two kinds of signals: deterministic and stochastic. Deterministic signals affect the values of timing residuals as a function of time, while stochastic signals affect the covariance matrix of the multivariate likelihood. Stochastic signals can be uncorrelated in time (white), which are described by the diagonal of a covariance matrix, and timecorrelated (red), which generally manifest as a random wandering of pulse arrival times.
White noise
Measured "white" noise parameters of pulsars  Phenomenological "white" noise parameters 


The above are factors that should be applied to uncertainty of arrival times (sigma_toa) in order to obtain a total white noise.  The above factors are physical sources of noise in PTA experiments. 
Red noise
Uncorrelated between pulsars  Correlated between pulsars 
Pulsar spin noise  irregularities in pulse ToA due to neutron star physics  Stochastic gravitationalwave background from supermassive binary black holes 
DM variations  they influence ToA due to interaction of radiowaves with electrons from interstellar medium. Noise PSD depends on radiofrequency.  Solar system ephemeris errors  errors in knowing positions and masses of celestial bodies in the Solar System. This noise can also be modelled as a deterministic process. 
Jumps, or phase jumps  errors arising from switching observing backends.  Clock errors 
Recent Work
We model red noise and link exponential dips in residuals with pulse shape changes