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Band-Limited Stochastic Processes in Discrete and Continuous Time

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  • David Stephen Pollock

Abstract

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

Suggested Citation

  • David Stephen Pollock, 2011. "Band-Limited Stochastic Processes in Discrete and Continuous Time," Discussion Papers in Economics 11/11, Division of Economics, School of Business, University of Leicester.
  • Handle: RePEc:lec:leecon:11/11
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    1. Adrian Pagan, 1997. "Towards an Understanding of Some Business Cycle Characteristics," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 30(1), pages 1-15, March.
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    1. D. Stephen G. Pollock, 2020. "Linear Stochastic Models in Discrete and Continuous Time," Econometrics, MDPI, vol. 8(3), pages 1-22, September.

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    Keywords

    Stochastic Differential Equations; Band-Limited Stochastic Processes; Aliasing and Interference;
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