Artist's sketch of accreting neutron star, a possible source of gravitational waves. Image: NASA.
Noise studies for Pulsar Timing Arrays
Millisecond pulsars are old neutron stars that has been spun up to a rotation period on the order of a millisecond. It is assumed that the spinup mechanism can be an accretion of matter. Another fact is that millisecond pulsars are not spinning down very much, comparing to other pulsars, according to ppdot diagram. Timing of radiopulsars from these neutron stars is very precice. Pulsar Timing Arrays are setups of radioobservatories recording residuals from timing models of millisecond pulars. Crosscorrelated timing residuals may indicate a presense of a stochastic gravitaitonalwave background in the nHz band, and should include the gravitationalwave background from merging galaxies in the observable Universe.
This is short note about noise properties of PTA, and it will probably expand in the future.
Useful dimensional relations and acronyms
 PSD  strain or noise power spectral density. Units:
 PTA  pulsar timing arrays
 ToA  pulse times of arrival
 DM  dispersion measure
Model for signals and noise
Likelihood function L(τ  θ) is a probability distribution of measured values (i.e. timing residuals τ) when noise and signals are present in the data. Their effect on a likelihood is described by parameters θ. In pulsar timing Likelihood is modelled as a multidimensional Gaussian distribution, where dimensions are related to residuals in each ToA measurement.
There are two kinds of signals: deterministic and stochastic. Deterministic signals affect the mean of L(τθ), while stochastic signals affect the standard deviation of our Gaussian distribution L(τθ).
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 signal  Stochastic gravitationalwave background from supermassive binary black holes :)  stochastic signal 
DM variations  they influence ToA due to interaction of radiowaves with electrons from interstellar medium. Noise PSD depends on radiofrequency, and can have a timevarying semiperiodic component (DM1 and DM2). In principle, can be subtracted.  stochastic signal  Solar system ephemeris errors  errors in knowing positions and masses of celestial bodies in our Solar system  deterministic signal 
Jumps, or phase jumps  errors arising from switching observing backends. This noise can be subtracted.  Clock errors 
Recent Work
Artist's representation of a GRB jets (NASA), and a 3D model of the Lomonosov satellite (MSU).