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

1987 ◽  
Vol 3 (1) ◽  
pp. 143-149 ◽  
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.

DERIVING THE EXACT DISCRETE ANALOG OF A CONTINUOUS TIME SYSTEM

2000 ◽  
Vol 16 (6) ◽  
pp. 998-1015 ◽  
Author(s):  
J. Roderick McCrorie
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Discrete Model ◽  
Space Form ◽  
Moving Average ◽  
Discrete Analog ◽  
Continuous Time Model ◽  
Time Model ◽  
Autoregressive Moving Average Model ◽  
Exact Discrete Model

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).

Gaussian Estimation of a Continuous Time Dynamic Model with Common Stochastic Trends

1996 ◽  
Vol 12 (2) ◽  
pp. 361-373 ◽  
Author(s):  
Theodore Simos
Keyword(s):  
Differential Equations ◽  
Continuous Time ◽  
Discrete Model ◽  
Likelihood Function ◽  
Order System ◽  
Time Dynamic ◽  
First Order ◽  
Stochastic Trends ◽  
Exact Discrete Model ◽  
Gaussian Estimation

We derive the exact discrete model and the Gaussian likelihood function of a first-order system of linear stochastic differential equations driven by an observable vector of stochastic trends and a vector of stationary innovations.

scholarly journals DISCRETE TIME REPRESENTATION OF CONTINUOUS TIME ARMA PROCESSES

2011 ◽  
Vol 28 (1) ◽  
pp. 219-238 ◽  
Author(s):  
Marcus J. Chambers ◽  
Michael A. Thornton
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time System ◽  
Time Model ◽  
Time Representation ◽  
Sunspot Data ◽  
Mixed Stock ◽  
Continuous Time System

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.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

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