Pulsar Timing Arrays (PTAs) aim to use ultra-stable millisecond pulsars (MSPs) to detect gravitational waves (GWs). The data that we use for the analysis comes from regular observations of an array of MSPs over decades of precision timing. All the information from a given observation is reduced to form a number of times of arrival (TOAs) of the radio signals. Comparing the predicted TOAs from our timing model against the measured TOAs gives us the residuals. These contain the imprint of GWs, but also other effects and sources of noise processes. All of which produce long-term/low-frequency variations in the residuals. In order to separate the GW signal from the noise we have to analyze an array of a large number of MSPs, to distinguish common processes, like from GWs, from the pulsar specific ones. For a gravitational wave background from a population of merging supermassive black hole binaries the characteristic signature is the Hellings-Downs (HD) correlation. It is quadrupolar in nature and therefore it can be confused with other types of correlations, eg. monopolar clock errors or dipolar solar system uncertainties. We thus have to focus our methods and tools on extracting this spatial signature of correlated red noise from the array of MSPs. Only with a definitive detection can we make new statements on the underlying astrophysics.
In my talk I will focus on the techniques that PTAs employ to analyze the data in order to extract a small signal amongst a lot of noise. I will use NANOGrav to form the basis and expand to other PTAs. The recent detection of a common amplitude red noise signal from the analysis of the 12.5 year dataset from the NANOGrav collaboration will be used as an example on how far we have come along and what still needs to be done. Parallel efforts from the European and Parkes PTAs are progressing as well and we hope that the efforts can be coordinated in the International PTA consortium to increase our sensitivity and expedite GW science with PTAs.