# Estimation and inference in univariate and multivariate log-GARCH-X models when the conditional density is unknown

*Genaro Sucarrat*,
*Steffen Grønneberg* and
*Alvaro Escribano* ()

*Computational Statistics & Data Analysis*, 2016, vol. 100, issue C, pages 582-594

**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.

**Keywords:** Log-GARCH-X; ARMA-X; Multivariate log-GARCH-X; VARMA-X; Volatility (search for similar items in EconPapers)

**Date:** 2016

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**Related works:**

Working Paper: Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown (2013)

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**Persistent link:** http://EconPapers.repec.org/RePEc:eee:csdana:v:100:y:2016:i:c:p:582-594

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