They are applied in some cases where data show evidence of non-stationarity, where an initial differencing step (corresponding to the "integrated" part of the model) can be applied to remove the non-stationarity.
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In signal processing, the multitaper method is a technique developed by David J. Thomson to estimate the power spectrum SX of a stationary ergodic finite-variance random process X, given a finite contiguous realization of X as data.