Template-type: ReDIF-Paper 1.0
Author-Name: Chia-Lin Chang
Author-Workplace-Name:
 Department of Applied Economics and Department of Finance National Chung Hsing University, Taiwan.
Author-Name:
 Michael McAleer
Author-Workplace-Name:
 Department of Quantitative Finance National Tsing Hua University, Taiwan and Econometric Institute Erasmus School of 
	Economics Erasmus University Rotterdam, The Netherlands and Department of Quantitative Economics Complutense University of 
	Madrid, Spain And Institute of Advanced Sciences Yokohama National University, Japan.
Title: The Fiction of Full BEKK: Pricing Fossil Fuels and Carbon Emissions
Abstract: The purpose of the paper is to (i) show that univariate GARCH is not a special case of multivariate GARCH, specifically the Full BEKK model, except 
	under parametric restrictions on the off-diagonal elements of the random coefficient autoregressive coefficient matrix, that are not consistent with 
	Full BEKK, and (ii) provide the regularity conditions that arise from the underlying random coefficient autoregressive process, for which the (quasi-) 
	maximum likelihood estimates (QMLE) have valid asymptotic properties under the appropriate parametric restrictions. The paper provides a discussion of 
	the stochastic processes that lead to the alternative specifications, regularity conditions, and asymptotic properties of the univariate and 
	multivariate GARCH models. It is shown that the Full BEKK model, which in empirical practice is estimated almost exclusively compared with Diagonal 
	BEKK (DBEKK), has no underlying stochastic process that leads to its specification, regularity conditions, or asymptotic properties, as compared with 
	DBEKK. An empirical illustration shows the differences in the QMLE of the parameters of the conditional means and conditional variances for the 
	univariate, DEBEKK and Full BEKK specifications.
Classification-JEL: C22, C32, C52, C58.
Keywords: Random coefficient stochastic process; Off-diagonal parametric restrictions; Diagonal BEKK; Full BEKK; Regularity conditions; Asymptotic properties; 
	Conditional volatility; Univariate and multivariate models; Fossil fuels and carbon emissions.
Length: 25 pages
Creation-Date: 2018-03
Number: 2018-08
X-File-Ref: http://america.sim.ucm.es/repec/ucm/ref/doicae1808.txt
File-URL: https://eprints.ucm.es/id/eprint/48487/1/1808.pdf
File-Format: Application/pdf
Handle: RePEc:ucm:doicae:1808