Semiparametric Estimation of Multivariate GARCH Models

Claudio Morana^1,2,3

¹Department of Economics, Management and Statistics, University of Milan-Bicocca, Milan, Italy.
²Center for Research on Pensions and Welfare Policies, Collegio Carlo Alberto, Moncalieri, Italy.
³Rimini Center for Economic Analysis, Rimini, Italy.

DOI: 10.4236/ojs.2015.57083                

Abstract

The paper introduces a new simple semiparametric estimator of the conditional variance-covariance and correlation matrix (SP-DCC). While sharing a similar sequential approach to existing dynamic conditional correlation (DCC) methods, SP-DCC has the advantage of not requiring the direct parameterization of the conditional covariance or correlation processes, therefore also avoiding any assumption on their long-run target. In the proposed framework, conditional variances are estimated by univariate GARCH models, for actual and suitably transformed series, in the first step; the latter are then nonlinearly combined in the second step, according to basic properties of the covariance and correlation operator, to yield nonparametric estimates of the various conditional covariances and correlations. Moreover, in contrast to available DCC methods, SP-DCC allows for straightforward estimation also for the non-symultaneous case, i.e. for the estimation of conditional cross-covariances and correlations, displaced at any time horizon of interest. A simple expost procedure to ensure well behaved conditional variance-covariance and correlation matrices, grounded on nonlinear shrinkage, is finally proposed. Due to its sequential implementation and scant computational burden, SP-DCC is very simple to apply and suitable for the modeling of vast sets of conditionally heteroskedastic time series.

Keywords

Multivariate GARCH Model, Dynamic Conditional Correlation, Semiparametric Estimation

Conflicts of Interest

The authors declare no conflicts of interest.

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