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.

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.

Gaussian Estimation of Mixed-Order Continuous-Time Dynamic Models with Unobservable Stochastic Trends from Mixed Stock and Flow Data

1997 ◽  
Vol 13 (4) ◽  
pp. 467-505 ◽  
Author(s):  
A.R. Bergstrom
Keyword(s):  
Continuous Time ◽  
Maximum Likelihood Estimates ◽  
Flow Data ◽  
Exogenous Variables ◽  
Time Dynamic ◽  
Stochastic Trends ◽  
Mixed Order ◽  
Mixed Stock ◽  
Gaussian Estimation ◽  
Order Continuous

This paper develops an algorithm for the exact Gaussian estimation of a mixed-order continuous-time dynamic model, with unobservable stochastic trends, from a sample of mixed stock and flow data. Its application yields exact maximum likelihood estimates when the innovations are Brownian motion and either the model is closed or the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under much more general circumstances. The paper includes detailed formulae for the implementation of the algorithm, when the model comprises a mixture of first- and second-order differential equations and both the endogenous and exogenous variables are a mixture of stocks and flows.

Open Higher Order Continuous-Time Dynamic Model with Mixed Stock and Flow Data and Derivatives of Exogenous Variables

1991 ◽  
Vol 7 (3) ◽  
pp. 404-408 ◽  
Author(s):  
K. Ben Nowman
Keyword(s):  
Continuous Time ◽  
Higher Order ◽  
Flow Data ◽  
Continuous Time Model ◽  
Exogenous Variables ◽  
Time Model ◽  
Time Dynamic ◽  
Mixed Stock ◽  
Gaussian Estimation ◽  
Derivatives Of

This paper is concerned with deriving formulae for higher order derivatives of exogenous variables for use in estimating the parameters of an open secondorder continuous time model with mixed stock and flow data and first and second order derivatives of exogenous variables which are not observable. This should provide the basis for the future estimation of continuous time models in a range of applied areas using the new Gaussian estimation computer program developed by Nowman [4].

A first order system of differential equations for covariant σ models

1979 ◽  
Vol 20 (12) ◽  
pp. 2619-2620
Author(s):  
C. Reina ◽  
M. Martellini ◽  
P. Sodano
Keyword(s):  
Differential Equations ◽  
Order System ◽  
System Of Differential Equations ◽  
First Order

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).

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