Mixed First‐ and Second‐Order Cointegrated Continuous Time Models with Mixed Stock and Flow Data

2019 ◽  
Vol 41 (2) ◽  
pp. 249-267
Author(s):  
Milena Hoyos
Keyword(s):  
Continuous Time ◽  
Second Order ◽  
Flow Data ◽  
Mixed Stock ◽  
Continuous Time Models

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.

scholarly journals THE EVOLUTION OF ONE- AND TWO-LOCUS SYSTEMS

Genetics ◽  
1976 ◽  
Vol 83 (3) ◽  
pp. 583-600
Author(s):  
Thomas Nagylaki
Keyword(s):  
Continuous Time ◽  
Time Derivative ◽  
Second Order ◽  
Rate Of Change ◽  
Evolutionary Significance ◽  
Multiple Alleles ◽  
Mean Fitness ◽  
The Mean ◽  
Change In Mean ◽  
Continuous Time Models

ABSTRACT Assuming age-independent fertilities and mortalities and random mating, continuous-time models for a monoecious population are investigated for weak selection. A single locus with multiple alleles and two alleles at each of two loci are considered. A slow-selection analysis of diallelic and multiallelic two-locus models with discrete nonoverlapping generations is also presented. The selective differences may be functions of genotypic frequencies, but their rate of change due to their explicit dependence on time (if any) must be at most of the second order in s, (i.e., O(s  2)), where s is the intensity of natural selection. Then, after several generations have elapsed, in the continuous time models the time-derivative of the deviations from Hardy-Weinberg proportions is of O(s  2), and in the two-locus models the rate of change of the linkage disequilibrium is of O(s  2). It follows that, if the rate of change of the genotypic fitnesses is smaller than second order in s (i.e., o(s  2)), then to O(s  2) the rate of change of the mean fitness of the population is equal to the genic variance. For a fixed value of s, however, no matter how small, the genic variance may occasionally be smaller in absolute value than the (possibly negative) lower order terms in the change in fitness, and hence the mean fitness may decrease. This happens if the allelic frequencies are changing extremely slowly, and hence occurs often very close to equilibrium. Some new expressions are derived for the change in mean fitness. It is shown that, with an error of O(s), the genotypic frequencies evolve as if the population were in Hardy-Weinberg proportions and linkage equilibrium. Thus, at least for the deterministic behavior of one and two loci, deviations from random combination appear to have very little evolutionary significance.

scholarly journals Reliable safety analysis with continuous-time models

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1022903-1022904
Author(s):  
Youdong Lin ◽  
Mark A. Stadtherr
Keyword(s):  
Continuous Time ◽  
Safety Analysis ◽  
Continuous Time Models
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