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Band-Limited Stochastic Processes in Discrete and Continuous Time

By D.S.G. Pollock

Abstract

A theory of band-limited linear stochastic processes is described and it is related\ud to the familiar theory of ARMA models in discrete time. By ignoring\ud the limitation on the frequencies of the forcing function, in the process of fitting\ud a conventional ARMA model, one is liable to derive estimates that are\ud severely biased. If the maximum frequency in the sampled data is less than the\ud Nyquist value, then the underlying continuous function can be reconstituted by\ud sinc function or Fourier interpolation. The estimation biases can be avoided by\ud re-sampling the continuous process at a rate corresponding to the maximum frequency\ud of the forcing function. Then, there is a direct correspondence between\ud the parameters of the band-limited ARMA model and those of an equivalent\ud continuous-time process

Topics: Stochastic Differential Equations, Band-Limited Stochastic Processes, Aliasing, Interference
Publisher: Dept. of Economics, University of Leicester
Year: 2011
OAI identifier: oai:lra.le.ac.uk:2381/9257

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Citations

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