The Fiction of Full BEKK: Pricing Fossil Fuels and Carbon Emissions

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 Ful...

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Detalles Bibliográficos
Autores: Chang, Chia-Lin, McAleer, Michael
Tipo de recurso: informe técnico
Fecha de publicación:2018
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/17428
Acceso en línea:https://hdl.handle.net/20.500.14352/17428
Access Level:acceso abierto
Palabra clave:C22
C32
C52
C58
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.
Econometría (Economía)
Indicadores económicos
5302 Econometría
5302.01 Indicadores Económicos
Descripción
Sumario: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.