Many post-processing algorithms have been developed in order to better separate the signal of a companion from the bright light of the host star, but the effect of such algorithms on the shape of exoplanet spectra extracted from integral field spectrograph data is poorly understood. The resulting spectra are affected by noise that is correlated in wavelength space due to both optical and data processing effects. Within the framework of Bayesian atmospheric retrievals, we aim to understand how these correlations and other systematic effects impact the inferred physical parameters. We consider three algorithms (KLIP, PynPoint, and ANDROMEDA), optimising the choice of algorithmic parameters using a series of injection tests on archival SPHERE and GPI data of the HR 8799 system. The wavelength-dependent covariance matrix was calculated to provide a measure of instrumental and algorithmic systematics. We perform atmospheric retrievals using petit RADTRANS on optimally extracted spectra to measure how these data processing systematics influence the retrieved parameter distributions. The choice of data processing algorithm and parameters significantly impact the accuracy of retrieval results, with the mean posterior parameter bias ranging from 1 to 3 σ from the true input parameters. Including the full covariance matrix in the likelihood improves the accuracy of the inferred parameters, and cannot be accounted for using ad hoc scaling parameters in the retrieval framework. Using the Bayesian information criterion and other statistical measures as heuristic goodness-of-fit metrics, the retrievals including the full covariance matrix are favoured when compared to using only the diagonal elements.
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