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

Understand

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 show that as the number of gravitational-wave detections grows, and as we gain access to more high signal-to-noise ratio events, this covariance will become a non-negligible source of systematic error.