Forecasting time-varying covariance with a robust Bayesian threshold model

The relationship between blood lactate concentration ([La]) and O2 uptake (VO2) during incremental exercise remains controversial: does [La] increase smoothly as a function of VO2 (continuous model), or does it begin to increase abruptly above a particular metabolic rate (threshold model)? The dynamic characteristics of the underlying physiological system are investigated using system identification analysis techniques. A multivariate deterministic time series model of the [La] and VO2 response to incremental changes in work rate was fitted to simulated and experimental data. Time-varying system response parameters were determined through the application of a weighted recursive least squares algorithm. The model, using the identified time-varying parameters, provided a good fit to the data. The variation of these parameters over time was then examined. Two major transitions in the parameters were found to occur at intensity levels equivalent to 53 +/- 8% and 77 +/- 9% maximal VO2 (experimental data). These changes in the model parameters indicate that the best linear dynamic model that fits the observed system behavior has changed. This implies that the system has changed its operation in some way, by altering its structure or by moving to a different operating region. The identified parameter changes over time suggest that the exercise intensity range (from rest to maximal VO2) is divided into three main intensity domains, each with distinct dynamics. Further study of this three-phase system may help in the understanding of the underlying physiological mechanisms that affect the dynamics of [La] and VO2 during exercise.

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Threshold models with time-varying threshold values and their application in estimating regime-sensitive Taylor rules

Studies in Nonlinear Dynamics & Econometrics ◽

10.1515/snde-2017-0114 ◽

2018 ◽

Vol 23 (5) ◽

Author(s):

Yanli Zhu ◽

Haiqiang Chen ◽

Ming Lin

Keyword(s):

Monte Carlo ◽

Regime Switching ◽

Latent Variable ◽

Threshold Model ◽

Threshold Value ◽

Time Varying ◽

Bayesian Approaches ◽

Taylor Rules ◽

Homogeneity Assumption ◽

Proposed Model

Abstract The literature of time series models with threshold effects makes the assumption of a constant threshold value over different periods. However, this time-homogeneity assumption tends to be too restrictive owing to the fact that the threshold value that triggers regime switching could possibly be time-varying. This study herein proposes a threshold model in which the threshold value is assumed to be a latent variable following an autoregressive (AR) process. The newly proposed model was estimated using a Markov Chain Monte Carlo (MCMC) algorithm under a Bayesian framework. The Monte Carlo simulations are presented to assess the effectiveness of the Bayesian approaches. An illustration of the model was made through an application to a regime-sensitive Taylor rule employing U.S. data.

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A Survey on Nonstrategic Models of Opinion Dynamics

Games ◽

10.3390/g11040065 ◽

2020 ◽

Vol 11 (4) ◽

pp. 65

Author(s):

Michel Grabisch ◽

Agnieszka Rusinowska

Keyword(s):

Threshold Model ◽

Opinion Dynamics ◽

Time Varying ◽

Binary Variable ◽

Rule Model ◽

Bounded Confidence ◽

Degroot Model ◽

Voter Models ◽

Time Varying Models ◽

Continuous Opinions

The paper presents a survey on selected models of opinion dynamics. Both discrete (more precisely, binary) opinion models as well as continuous opinion models are discussed. We focus on frameworks that assume non-Bayesian updating of opinions. In the survey, a special attention is paid to modeling nonconformity (in particular, anticonformity) behavior. For the case of opinions represented by a binary variable, we recall the threshold model, the voter and q-voter models, the majority rule model, and the aggregation framework. For the case of continuous opinions, we present the DeGroot model and some of its variations, time-varying models, and bounded confidence models.

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