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In many dynamic systems such as aircraft, space vehicles, nuclear power plants, and magnetohydrodynamic (MHD) generators, it is often necessary to determine the cause of fluctuations in a primary variable as a function of dynamic inputs to the system and other process variables. The timely detection of the source of an anomaly in the system is useful in preventing damage to the system and restoring it to a normal operational mode. Multivariate empirical time-series models are developed in various forms and applied to system diagnostics. Proper combination of multiple-input single-output (MISO) models and multivariate feedback models are shown to give useful cause-effect relationships among dynamic variables. Recursive methods of estimating successively higher order models (not time recursion) and causal flow maps are developed and applied to the diagnosis of fluctuations in the output voltage of an open-cycle magnetohydrodynamic generator.