We present a new method of testing analog circuits based on spectral estimation using auto regressive moving average (ARMA) models. We use a tiered testing approach where each tier becomes progressively more computationally expensive. Badly damaged circuits are quickly eliminated without wasting tester time. The models are generated using input and output analog circuit samples. Results are presented for two passive filters and an active multiplier/modulator. The first two levels of the tiered testing approach use model parameters and the third tier estimates the spectral content of the circuits? output. Incorporating this method into an analog/mixed-signal built-in-self-test (BIST) environment is also discussed, including hardware overhead and general implementation. Our 3-tiered ARMA testing method was highly effective, had 0% yield loss, and achieved low defect level of 0.0821514 on a population of 28,290 circuit variations generated by Monte-Carlo analysis.