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Some benefits of aliasing in time series analysis

The problem of sampling a signal with interval T is present in preparing continuous-time processes for discrete-time signal processing algorithms and in down-sampling a discrete-time signal to a larger time scale. The important issue is whether invariance in time or in frequency domain is preferred. The time domain approach preserves the covariance function at time shifts KT, while the frequency domain approach tries to preserve the part of the original spectrum up to frequency π/T. This requires the use of non-ideal anti-aliasing filters, which will be harmful in time series analysis because the product of the process and the anti-aliasing filter is modeled.