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Recently, a method has been developed for detecting and quantifying the time variation in frequency response function (FRF) measurements using arbitrary excitations. The following basic assumptions have been made: 1) The input is known exactly (generalized output error stochastic framework), and 2) the time-variant system operates in an open loop. The latter excludes any interaction between the time-variant system and the generator/actuator. In this paper, we extend the results of the work by Pintelon to noisy input-output observations (errors-in-variables stochastic framework) of time-variant systems operating in a closed loop.