DERIVING THE EXACT DISCRETE ANALOG OF A CONTINUOUS TIME SYSTEM

The exact discrete model satisfied by equispaced data generated by a linear stochastic differential equations system is derived by a method that does not imply restrictions on observed discrete data per se. The method involves integrating the solution of the continuous time model in state space form and a nonstandard change in the order of three types of integration, facilitating the representation of the exact discrete model as an asymptotically time-invariant vector autoregressive moving average model. The method applying to the state space form is general and is illustrated using the prototypical higher order model for mixed stock and flow data discussed by Bergstrom (1986, Econometric Theory 2, 350–373).

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An Exact Discrete Analog to a Closed Linear First-Order Continuous-Time System with Mixed Sample

Econometric Theory ◽

10.1017/s0266466600004163 ◽

1987 ◽

Vol 3 (1) ◽

pp. 143-149 ◽

Cited By ~ 16

Author(s):

Terence D. Agbeyegbe

Keyword(s):

Continuous Time ◽

Discrete Model ◽

Moving Average ◽

Discrete Analog ◽

Time System ◽

First Order ◽

Exact Discrete Model ◽

Asymptotically Efficient ◽

Order Continuous ◽

Continuous Time System

This article deals with the derivation of the exact discrete model that corresponds to a closed linear first-order continuous-time system with mixed stock and flow data. This exact discrete model is (under appropriate additional conditions) a stationary autoregressive moving average time series model and may allow one to obtain asymptotically efficient estimators of the parameters describing the continuous-time system.

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A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components

10.1063/1.3498530 ◽

2010 ◽

Author(s):

F. E. Benth ◽

S. Koekebakker ◽

V. Zakamouline ◽

Theodore E. Simos ◽

George Psihoyios ◽

...

Keyword(s):

Interest Rate ◽

Continuous Time ◽

Moving Average ◽

Continuous Time Model ◽

Time Model

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A discrete epidemic model for bovine Babesiosis disease and tick populations

Open Physics ◽

10.1515/phys-2017-0040 ◽

2017 ◽

Vol 15 (1) ◽

pp. 360-369 ◽

Cited By ~ 9

Author(s):

Diego F. Aranda ◽

Deccy Y. Trejos ◽

Jose C. Valverde

Keyword(s):

Continuous Time ◽

Discrete Model ◽

Theoretical Study ◽

Biological Significance ◽

Bovine Babesiosis ◽

Continuous Time Model ◽

Time Model ◽

Discrete Epidemic Model ◽

Discrete Methods ◽

Model Subject

AbstractIn this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.

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ESTIMATING CONTINUOUS-TIME MODELS ON THE BASIS OF DISCRETE DATA VIA AN EXACT DISCRETE ANALOG

Econometric Theory ◽

10.1017/s0266466608090452 ◽

2009 ◽

Vol 25 (4) ◽

pp. 1120-1137 ◽

Cited By ~ 9

Author(s):

J. Roderick McCrorie

Keyword(s):

Time Series ◽

Discrete Time ◽

Continuous Time ◽

Financial Time Series ◽

Discrete Data ◽

Discrete Analog ◽

Continuous Time Model ◽

Time Model ◽

Financial Time ◽

Time Modeling

This paper offers a perspective on A.R. Bergstrom’s contribution to continuous-time modeling, focusing on his preferred method of estimating the parameters of a structural continuous-time model using an exact discrete-time analog. Some inherent difficulties in this approach are discussed, which help to explain why, in spite of his prescience, the methods around his time were not universally adopted as he had hoped. Even so, it is argued that Bergstrom’s contribution and legacy is secure and retains some relevance today for the analysis of macroeconomic and financial time series.

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