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Stochastic processes of limited frequency and the effects of oversampling

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  • Pollock, D.S.G.

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.

Suggested Citation

  • Pollock, D.S.G., 2018. "Stochastic processes of limited frequency and the effects of oversampling," Econometrics and Statistics, Elsevier, vol. 7(C), pages 18-29.
    • Handle: RePEc:eee:ecosta:v:7:y:2018:i:c:p:18-29
    DOI: 10.1016/j.ecosta.2016.12.003
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    1. Alex S. Morton & Granville Tunnicliffe‐Wilson, 2004. "A class of modified high‐order autoregressive models with improved resolution of low‐frequency cycles," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 235-250, March.
    2. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    3. Proietti, Tommaso, 2008. "Band spectral estimation for signal extraction," Economic Modelling, Elsevier, vol. 25(1), pages 54-69, January.
    4. J. Haywood & G. Tunnicliffe Wilson, 1997. "Fitting Time Series Models by Minimizing Multistep‐ahead Errors: a Frequency Domain Approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 237-254.
    5. 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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