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THE EXACT DISCRETE MODEL OF A THIRD-ORDER SYSTEM OF LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH OBSERVABLE STOCHASTIC TRENDS

Published online by Cambridge University Press:  14 October 2009

Theodore Simos
Theodore Simos*
Affiliation:
University of Ioannina
*
Address correspondence to: Theodore Simos, Department of Economics, University Campus, University of Ioannina, 45110 Ioannina, Greece; e-mail: tsimos@cc.uoi.gr.
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Abstract

The objective of this paper is to develop closed-form formulae for the exact discretization of a third-order system of stochastic differential equations, with fixed initial conditions, driven by observable stochastic trends and white noise innovations. The model provides a realistic alternative to first- and second-order differential equation specifications of the time lag distribution, forming the basis of a testing and estimation procedure. The exact discrete models, derived under two sampling schemes with either stock or flow variables, are put into a system error correction form that preserves the information of the underlying continuous time model regarding the order of integration and the dimension of cointegration space.

Keywords

Continuous Time ModelsExact DiscretizationStochastic Trends
Type
Articles
Information
Macroeconomic Dynamics , Volume 13 , Issue 5 , November 2009 , pp. 656 - 672
Copyright
Copyright © Cambridge University Press 2009

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