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The Discrete–Continuous Correspondence for Frequency-Limited Arma Models and the Hazards of Oversampling

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  • David Stephen Pollock

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 ? 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 will cause the ARMA estimates to be severely biased. The paper reveals the nature of these problems and it shows how they may be overcome. It is argued that the estimation of macroeconomic processes may be compromised by a failure to take account of their limits in frequency.

Suggested Citation

  • David Stephen Pollock, 2011. "The Discrete–Continuous Correspondence for Frequency-Limited Arma Models and the Hazards of Oversampling," Discussion Papers in Economics 11/14, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:11/14
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    Keywords

    Stochastic Differential Equations; Band-Limited Stochastic Processes; Oversampling;
    All these keywords.

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