Inference with finite time series: Observing the gravitational Universe through windows

Time series analysis is ubiquitous in many fields of science including gravitational-wave astronomy, where strain time series are analyzed to infer the nature of gravitational-wave sources, e.g., black holes and neutron stars. It is common in gravitational-wave transient studies to apply a tapered window function to reduce the effects of spectral artifacts from the sharp edges of data segments. We show that the conventional analysis of tapered data fails to take into account covariance between frequency bins, which arises for all finite time series-no matter the choice of window function. We discuss the origin of this covariance and derive a framework that models the correlation induced by the window function. We demonstrate this solution using both simulated Gaussian noise and real Advanced LIGO/Advanced Virgo data. We show that the effect of these correlations is similar in scale to widely studied systematic errors, e.g., uncertainty in detector calibration and power spectral density estimation.