# Abstract for:

Deriving the Exact Discrete Analog of a Continuous Time System

J R McCrorie,
December 1997

Paper No' EM/1997/343:

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**Keywords:** continuous time; exact discrete model; random measure; matrix exponential

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**Is hard copy/paper copy available?** NO - Paper Copy Out Of Print.

This Paper is published under the following series:
**Econometrics**

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## Abstract:

We present a method of deriving the exact discrete model satisfied by equispaced data generated by a system of linear stochastic differential equations without implying the usual restrictions on observed discrete data that are capable of being rejected by a statistical test. The method involves integrating the solution of the continuous time model in state space form, and relies on a non-standard change in the order of three types of integration as a means of representing the exact discrete model as an asymptotically time-invariant VARMA model. Applying to the state space form of the model, the method is general, and delivers a parsimonious representation of the exact discrete model in any particular case. It is applied by way of example to the prototypical higher order model for mixed stock and flow data discussed by Bergstrom (1986, Econometric Theory 2, 350-373.