Stochastic processes of limited frequency and the effects of oversampling

Abstract

Discrete-time ARMA processes can be placed in a one-to-one correspondence with a set of continuous-time processes that are bounded in frequency by the Nyquist value of π radians per sample period. It is well known that, if data are sampled from a continuous process of which the maximum frequency exceeds the Nyquist value, then there will be a problem of aliasing. However, if the sampling is too rapid, then other problems will arise that may cause the ARMA estimates to be severely biased. The paper reveals the nature of these problems and it shows how they may be overcome.