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...
| Autores: | , |
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| 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 |
| 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. |
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