Econometric Theory

MISCELLANEA

DISCRETE TIME REPRESENTATION OF CONTINUOUS TIME ARMA PROCESSES

Marcus J. Chambersa1 c1 and Michael A. Thorntona2

a1 University of Essex

a2 University of Reading

Abstract

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

(Online publication August 02 2011)

Correspondence

c1 Address correspondence to Marcus J. Chambers, Department of Economics, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, United Kingdom; e-mail: mchamb@essex.ac.uk.

Footnotes

The second author’s research was supported by an Economic and Social Research Council studentship (PTA-030-2006-00395). We thank the editor, Peter Phillips, and two anonymous referees for helpful comments.

Metrics