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This paper proposes a fault detection method for multivariate signals. The method assesses whether or not the multivariate autocovariance functions of two independently sampled system signals coincide. If the first signal is known to be sampled from a well-functioning system, then rejection of signal equality is tantamount to concluding that the second signal is sampled from a faulty system. The proposed method is based on the asymptotic properties of the periodogram of multivariate stationary time series and is nonparametric in nature; in particular, there is no need to model the signals under study, an often arduous task. Several natural and synthetic faults were introduced in a Solar Turbines Mercury 50 4.5 MW gas turbine and the resulting compressor delivery pressure and generated electrical power were analyzed. The proposed method capably detected all faults.