Pulsar timing analysis in the presence of correlated noise

By William A. Coles, G. Hobbs, David J. Champion, R. Manchester, J. Verbiest. 2011

152 citations recorded by the source corpus.

Pulsar timing observations are usually analysed with least-squares fitting procedures under the assumption that the timing residuals are uncorrelated (statistically ‘white’). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/cc4e5de33c1004858935b906ae0e79decb9a9c66

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In Astronomy and Astrophysics

Citations in the corpus

Development of a Pulsar-Based Time-Scale (2012, methodology): “…from https://academ ic.oup.com /m nras/article-abstract/427/4/2780/971096 by C alifornia Institute of Technology user on 07 D ecem ber 2018 a generalized least-squares fitting procedure (Coles et al. 2011) to account for the timing noise when fitting the pulsar timing model and the c(t) parameters.”
THE NANOGRAV NINE-YEAR DATA SET: OBSERVATIONS, ARRIVAL TIME MEASUREMENTS, AND ANALYSIS OF 37 MILLISECOND PULSARS (2015, methodology): “…approach, it has several drawbacks: first, in the presence of unmodeled red noise, this can introduce systematic biases in other parameters (see for example discussion in Coles et al. 2011); this can be mitigated via improved noise modeling as described in Section 5 and references therein.”
The International Pulsar Timing Array: First Data Release (2016, methodology): “…which includes jumps, EFACs, TEMPO2-format EQUADs (i.e. following equation 5), a DM model implemented through DM-offset flags (‘-dmo’) added to the ToA lines, a red-noise model in the form of a spectral model compatible with the Cholesky TEMPO2 code introduced by Coles et al. (2011), but no ECORRs.”
The Parkes Pulsar Timing Array (2009, methodology): “This led to Coles et al. (2011) which described how pulsar data sets should be analysed when affected by red noise.”
Detection of 107 glitches in 36 southern pulsars (2012, methodology): “We fitted for these parameters using the “Cholesky” method that accounts for the effects of correlated noise (Coles et al. 2011).”
The Parkes Pulsar Timing Array Project (2006, methodology): “Cholesky whitening (Coles et al. 2011) is used to properly account for the correlation in the residuals and thus to provide reliable error estimates for the DM variations and other parameters.”