scholarly journals Estimation and Properties of a Time-Varying GQARCH(1,1)-M Model

2011 ◽  
Vol 2011 ◽  
pp. 1-39 ◽  
Author(s):  
Sofia Anyfantaki ◽  
Antonis Demos
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Em Algorithm ◽  
Sample Size ◽  
Dynamic Properties ◽  
Conditional Variance ◽  
Monte Carlo Algorithm ◽  
Time Varying ◽  
Likelihood Analysis

Time-varying GARCH-M models are commonly used in econometrics and financial economics. Yet the recursive nature of the conditional variance makes exact likelihood analysis of these models computationally infeasible. This paper outlines the issues and suggests to employ a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a simulated Bayesian solution in only computational operations, where is the sample size. Furthermore, the theoretical dynamic properties of a time-varying GQARCH(1,1)-M are derived. We discuss them and apply the suggested Bayesian estimation to three major stock markets.

scholarly journals Estimation of trace gas fluxes with objectively determined basis functions using reversible-jump Markov chain Monte Carlo

2016 ◽  
Vol 9 (9) ◽  
pp. 3213-3229 ◽  
Author(s):  
Mark F. Lunt ◽  
Matt Rigby ◽  
Anita L. Ganesan ◽  
Alistair J. Manning
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Spatial Domain ◽  
Monte Carlo Algorithm ◽  
Trace Gas ◽  
Reversible Jump ◽  
Pseudo Data ◽  
Atmospheric Trace Gas

Abstract. Atmospheric trace gas inversions often attempt to attribute fluxes to a high-dimensional grid using observations. To make this problem computationally feasible, and to reduce the degree of under-determination, some form of dimension reduction is usually performed. Here, we present an objective method for reducing the spatial dimension of the parameter space in atmospheric trace gas inversions. In addition to solving for a set of unknowns that govern emissions of a trace gas, we set out a framework that considers the number of unknowns to itself be an unknown. We rely on the well-established reversible-jump Markov chain Monte Carlo algorithm to use the data to determine the dimension of the parameter space. This framework provides a single-step process that solves for both the resolution of the inversion grid, as well as the magnitude of fluxes from this grid. Therefore, the uncertainty that surrounds the choice of aggregation is accounted for in the posterior parameter distribution. The posterior distribution of this transdimensional Markov chain provides a naturally smoothed solution, formed from an ensemble of coarser partitions of the spatial domain. We describe the form of the reversible-jump algorithm and how it may be applied to trace gas inversions. We build the system into a hierarchical Bayesian framework in which other unknown factors, such as the magnitude of the model uncertainty, can also be explored. A pseudo-data example is used to show the usefulness of this approach when compared to a subjectively chosen partitioning of a spatial domain. An inversion using real data is also shown to illustrate the scales at which the data allow for methane emissions over north-west Europe to be resolved.

scholarly journals Fitting Spectral Energy Distributions of AGN A Markov Chain Monte Carlo Approach

2013 ◽  
Vol 9 (S304) ◽  
pp. 228-229
Author(s):  
Gabriela Calistro Rivera ◽  
Elisabeta Lusso ◽  
Joseph F. Hennawi ◽  
David W. Hogg
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Galactic Nuclei ◽  
Physical Models ◽  
Monte Carlo Algorithm ◽  
Spectral Energy ◽  
Spectral Energy Distributions ◽  
Energy Distributions ◽  
Multiple Parameters

AbstractWe present AGNfitter: a Markov Chain Monte Carlo algorithm developed to fit the spectral energy distributions (SEDs) of active galactic nuclei (AGN) with different physical models of AGN components. This code is well suited to determine in a robust way multiple parameters and their uncertainties, which quantify the physical processes responsible for the panchromatic nature of active galaxies and quasars. We describe the technicalities of the code and test its capabilities in the context of X-ray selected obscured AGN using multiwavelength data from the XMM-COSMOS survey.

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