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Sampling Dynamical Systems

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  • Hinich, Melvin J.

Abstract

Linear dynamical systems are widely used in many different fields from engineering to economics. One simple but important class of such systems is called the single-input transfer function model. Suppose that all variables of the system are sampled for a period using a fixed sample rate. The central issue of this paper is the determination of the smallest sampling rate that will yield a sample that will allow the investigator to identify the discrete-time representation of the system. A critical sampling rate exists that will identify the model. This rate, called the Nyquist rate, is twice the highest frequency component of the system. Sampling at a lower rate will result in an identification problem that is serious. The standard assumptions made about the model and the unobserved innovation errors in the model protect the investigators from the identification problem and resulting biases of undersampling. The critical assumption that is needed to identify an undersampled system is that at least one of the exogenous time series be white noise.

Suggested Citation

  • Hinich, Melvin J., 1999. "Sampling Dynamical Systems," Macroeconomic Dynamics, Cambridge University Press, vol. 3(4), pages 602-609, December.
    • Handle: RePEc:cup:macdyn:v:3:y:1999:i:04:p:602-609_01
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    Cited by:

    1. Òscar Jordà & Massimiliano Marcellino, 2004. "Time‐scale transformations of discrete time processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 873-894, November.
    2. Oscar Jordà & Massimiliano Marcellino, 2004. "Time-scale transformations of discrete time processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 873-894, November.

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