Publication: Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown
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2016-08-01
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Elsevier
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Abstract
A general framework for the estimation and inference in univariate and multivariate Generalised log-ARCH-X (i.e. log-GARCH-X) models when the conditional density is unknown is proposed. The framework employs (V)ARMA-X representations and relies on a bias-adjustment in the log-volatility intercept. The bias is induced by (V)ARMA estimators, but the remaining parameters can be estimated in a consistent and asymptotically normal manner by usual (V)ARMA methods. An estimator of the bias and a closed-form expression for the asymptotic variance is derived. Adding covariates and/or increasing the dimension of the model does not change the structure of the problem, so the univariate bias adjustment procedure is applicable not only in univariate log-GARCH-X models estimated by the ARMA-X representation, but also in multivariate log-GARCH-X models estimated by VARMA-X representations. Extensive simulations verify the properties of the log-moment estimator, and an empirical application illustrates the usefulness of the methods. (C) 2015 Elsevier B.V. All rights reserved.
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Log-garch-x, Arma-x, Multivariate log-garch-x, Varma-x, Maximum-likelihood-estimation, Asymptotic theory, Volatility, Heteroskedasticity, Prices
Bibliographic citation
Sucarrat, G., Grønneberg, S. and Escribano, A. (2016). Estimation and inference in univariate and multivariate log- GARCH-X models when the conditional density is unknown. Computational Statistics & Data Analysis, v. 100, pp. 582-594.