Pulsar timing analysis in the presence of correlated noise

TL;DR

This paper presents an optimal method for pulsar timing analysis that accounts for correlated noise by estimating the residuals' covariance matrix and applying a whitening transformation, improving parameter estimation accuracy.

Contribution

It introduces a covariance matrix estimation technique and a whitening transformation based on Cholesky decomposition for optimal pulsar timing analysis with correlated noise.

Findings

The method accurately estimates the covariance matrix of residuals.

The whitening transformation improves parameter estimation in correlated noise environments.

Applicable to irregular sampling and variable error bars.

Abstract

Pulsar timing observations are usually analysed with least-square-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.