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DISCRETE TIME REPRESENTATION OF CONTINUOUSTIME ARMA PROCESSES

Published online by Cambridge University Press:  02 August 2011

Marcus J. Chambers and
Michael A. Thornton
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Abstract

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This paper derives exact discrete time representationsfor data generated by a continuous timeautoregressive moving average (ARMA) system withmixed stock and flow data. The representations forsystems comprised entirely of stocks or of flows arealso given. In each case the discrete timerepresentations are shown to be of ARMA form, theorders depending on those of the continuous timesystem. Three examples and applications are alsoprovided, two of which concern the stationaryARMA(2, 1) model with stock variables (withapplications to sunspot data and a short-terminterest rate) and one concerning the nonstationaryARMA(2, 1) model with a flow variable (with anapplication to U.S. nondurable consumers’expenditure). In all three examples the presence ofan MA(1) component in the continuous time system hasa dramatic impact on eradicating unaccounted-forserial correlation that is present in the discretetime version of the ARMA(2, 0) specification, eventhough the form of the discrete time model isARMA(2, 1) for both models.

Information

Type
Brief Report
Information
Econometric Theory , Volume 28 , Issue 1 , February 2012, pp. 219 - 238
Copyright
Copyright © Cambridge University Press 2011

Footnotes

The second author’s research was supported by anEconomic and Social Research Council studentship(PTA-030-2006-00395). We thank the editor, PeterPhillips, and two anonymous referees for helpfulcomments.

References

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