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...s for the factors. One could in principle also consider stochastic volatility as an alternative to the GARCH-type models (see e.g. Doz and Renault ∗Corresponding author. Address: Department of Quantitative Economics, Universiteit van Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands. E-mail: H.P.Boswijk@uva.nl. †E-mail: rvanderweide@worldbank.org. 1 (2006)). For surveys on multivariate volatility models we refer to e.g. Bauwens et al. (2006), and Silvennoinen and Terasvirta (2008); for an overview on common features, see Urga (2007), and for a glossary to volatility models, see Bollerslev (2008). The model is designed to balance generality against ease of estimation. Time-varying variances, time-varying correlations and (asymmetric) volatility spillovers are accommodated, which denote the key stylized facts of multivariate financial data. Moreover, the model is closed under linear transformations (i.e. one does not leave the model when rebalancing ones portfolios) and is closed under temporal aggregation, which makes the model analytically convenient. (For temporal aggregation results for multivariate GARCH models, see Hafner (2008).) van der Weide (2002) proposed a two-step estimati...

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...ndex (VXO) used in Bloom (2009), and interest rate spreads (see Bekaert, Hoerova, and Lo Duca, 2012, for a discussion). However, the calculation of GARCH and SV measures necessitates an explicit formulation of the data generating process. The estimation of the model calls for a wellspecified time series process of the variable under concern, and each model has to pass a battery of specification tests (Lundbergh and Teräsvirta, 2002). To avoid misspecification, innumerable extensions of the basic GARCH and SV model have been proposed to meet the specific requirements of a certain variable (see Bollerslev, 2009, for an overview). Finally, convergence of the estimation has to be ensured. Since we consider a multitude of time series there is a significant drawback associated with GARCH and SV models. This drawback can, however, be overcome by using a basic data driven filter which enables us to measure the uncertainty surrounding an individual variable in a transparent and robust manner. A straightforward proxy for uncertainty may be obtained when we estimate the variance of a variable within a rolling window (Andersen, Bollerslev, Christoffersen, and Diebold, 2006). However, such an estimator suffers...

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... past negative and positive innovations. Defining as the log-return of stock index i in r country at time t, the AR (1) -tTGARCH(1,1) model can be written as : Where denotes the indicator function, : degree of freedom of t-distribution. When estimating the TGARCH model with equity index returns, γ is typically found to be positive, so that the volatility increases proportionally more following negative than positive shocks. This asymmetry is sometimes referred to in the literature as a “leverage effect,” although it is now widely agreed that it has little to do with actual financial leverage (Bollerslev, 2008). 2.2. Copula Specifications and Dependence Measures We employ various copula functions that are frequently applied in finance, offering different dependence structures. Trivially speaking, tail dependence expresses the probability of having a high (low) extreme value of Y given that a high (low) extreme value of X has occurred. The analytic form for the coefficient of upper tail dependence ( U ) is 1 1 U 1 lim Y Xy x u P F u F u provided that the random variables X and Y are asymptotically dependent while U (0,1] , on the contrary, if U 0 , then X and Y are asymp...