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Stochastic processes of limited frequency and the effects of oversampling

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  • D.S.G. 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 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

  • D.S.G. Pollock, 2017. "Stochastic processes of limited frequency and the effects of oversampling," Discussion Papers in Economics 17/03, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:17/03
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    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp17-03.pdf
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    References listed on IDEAS

    as
    1. D.S.G. Pollock, 2008. "Realisations of Finite-Sample Frequency-Selective Filters," Discussion Papers in Economics 08/32, Division of Economics, School of Business, University of Leicester.
    2. Proietti, Tommaso, 2008. "Band spectral estimation for signal extraction," Economic Modelling, Elsevier, vol. 25(1), pages 54-69, January.
    3. 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.
    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.
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    Cited by:

    1. D.S.G. Pollock, "undated". "Linear Stochastic Models in Discrete and Continuous Time," Discussion Papers in Economics 19/10, Division of Economics, School of Business, University of Leicester.

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    More about this item

    Keywords

    ARMA Modelling; Stochastic Differential Equations; Frequency-Limited Stochastic Processes; Oversampling;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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