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].

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.

The Estimation of Open Higher-Order Continuous Time Dynamic Models with Mixed Stock and Flow Data

1986 ◽  
Vol 2 (3) ◽  
pp. 350-373 ◽  
Author(s):  
A. R. Bergstrom
Keyword(s):  
Maximum Likelihood ◽  
Continuous Time ◽  
Dynamic Models ◽  
Higher Order ◽  
Maximum Likelihood Estimates ◽  
Order System ◽  
Exogenous Variables ◽  
Time Dynamic ◽  
Mixed Stock ◽  
Order Continuous

This article extends recent work on the Gaussian or quasi-maximum likelihood estimation of the parameters of a closed higher-order continuous time dynamic model by introducing exogenous variables into the model The method presented yields exact maximum likelihood estimates when the innovations are Gaussian and the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under more general conditions. It is applicable, in principle, to a system of any order with mixed stock and iow data. The precise formulas for its implementation are derived, in this article, for a second-order system in which both the endog-enous and exogenous variables are a mixture of stock and flow variables.

DISCRETE TIME REPRESENTATIONS OF COINTEGRATED CONTINUOUS TIME MODELS WITH MIXED SAMPLE DATA

2009 ◽  
Vol 25 (4) ◽  
pp. 1030-1049 ◽  
Author(s):  
Marcus J. Chambers
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Time System ◽  
Time Model ◽  
Stochastic Trends ◽  
Sample Data ◽  
Flow Variables ◽  
Mixed Stock ◽  
Gaussian Estimation ◽  
Continuous Time System

This paper derives an exact discrete time representation corresponding to a triangular cointegrated continuous time system with mixed stock and flow variables and observable stochastic trends. The discrete time model inherits the triangular structure of the underlying continuous time system and does not suffer from the apparent excess differencing that has been found in some related work. It can therefore serve as a basis for the study of the asymptotic sampling properties of estimators of the model's parameters. Some further analytical and computational results that enable Gaussian estimation to be implemented are also provided.

scholarly journals Booms and Busts in the Oil Market: Identifying Speculative Bubbles Using a Continuous-Time Dynamic System

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kaizhi Yu ◽  
Yun Zhang
Keyword(s):  
Continuous Time ◽  
Oil Prices ◽  
Time Varying ◽  
Continuous Time Model ◽  
Time Model ◽  
Time Dynamic ◽  
Speculative Bubbles ◽  
Economic Fundamentals ◽  
Oil Market ◽  
Popular View

The sharp changes in oil prices since 2004 featured a nonlinear data-generating mechanism which displayed bubble-like behavior. A popular view is that such a salient pattern cannot be explained by shifts in economic fundamentals, but was driven by speculative bubbles as a consequence of the increased financialization of oil future markets. Testing this hypothesis, however, is challenging since the fundamental component of the oil price is unobservable. This paper attempts to isolate the contribution of speculative bubbles and fundamentals to the evolution of oil prices by providing a stylized model of commodity pricing. Motivated by our theoretical model, we adopt a continuous-time model with a random and time-varying persistence parameter to empirically investigate the presence of speculative bubbles in daily oil future prices over the period April 1983 to June 2020. We do not find any evidence in favor of speculative bubbles, although we indeed find that oil prices exhibit episodes of unstable behavior after 2004.

The Estimation of Parameters in Nonstationary Higher Order Continuous-Time Dynamic Models

1985 ◽  
Vol 1 (3) ◽  
pp. 369-385 ◽  
Author(s):  
A. R. Bergstrom
Keyword(s):  
Continuous Time ◽  
Iterative Procedure ◽  
Dynamic Models ◽  
Structural Parameters ◽  
Higher Order ◽  
Estimation Of Parameters ◽  
Initial State ◽  
Time Dynamic ◽  
Mixed Stock ◽  
Order Continuous

This paper is concerned with derivation of a new efficient algorithm for computing the exact Gaussian likelihood for structural parameters in nonstationary higher-order continuous-time dynamic models and with its application in the estimation of these parameters. The algorithm completely avoids the computation of the covariance matrix of the observations and is applicable to a system of any order with mixed stock and flow data. It is used as the basis for an iterative procedure in which the structural parameters and the initial state vector are estimated alternately.

scholarly journals Gaussian Estimation of One-Factor Mean Reversion Processes

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Freddy H. Marín Sánchez ◽  
J. Sebastian Palacio
Keyword(s):  
Maximum Likelihood ◽  
Continuous Time ◽  
Simulated Data ◽  
Mean Reversion ◽  
Data Series ◽  
Continuous Time Model ◽  
Time Model ◽  
New Process ◽  
Gaussian Estimation ◽  
Maximum Likelihood Technique

We propose a new alternative method to estimate the parameters in one-factor mean reversion processes based on the maximum likelihood technique. This approach makes use of Euler-Maruyama scheme to approximate the continuous-time model and build a new process discretized. The closed formulas for the estimators are obtained. Using simulated data series, we compare the results obtained with the results published by other authors.

Sign in / Sign up

Export Citation Format

Share Document