Identification of structural multivariate GARCH models

Abstract

Multivariate GARCH models are widely used to model volatility and correlation dynamics of financial time series. These models are typically silent about the transmission of implied orthogonalized shocks to vector returns. We propose a loss statistic to discriminate in a data-driven way between alternative structural assumptions about the transmission scheme. In its structural form, a four dimensional system comprising US and Latin American stock market returns points to a substantial volatility transmission from the US to the Latin American markets. The identified structural model improves the estimation of classical measures of portfolio risk,as well as corresponding variations.

Dynamic Score-Driven Independent Component Analysis

“…Then, by Theorem 2 of Hafner et al (2020), the conditional kurtosis of portfolio returns is a non-trivial function of δ t and given by K t (δ t , w t ) = ς t (δ t , w t )/σ 4 t , where…”

“…Hafner and Herwartz (2006) used the identification of independent components to define unique volatility impulse response functions. Recently, Hafner et al (2020) have suggested to identify MGARCH models by means of a static rotation of ad-hoc identification schemes such as spectral or Cholesky decompositions.…”

Asymptotic and Finite Sample Properties for Multivariate Rotated GARCH Models

“…Figure 8 supports the result of the Engle and Colacito (2006) test in Table 4. To improve the forecasting performance, we may consider a more general rotation matrix, as in Asai and McAleer (2020) and Hafner et al (2020). 15), while the dotted lines indicate the confidence interval.…”

“…While these authors attempt to find orthogonal or unconditionally uncorrelated components in the raw returns, which can then be modeled individually through univariate variance models, Noureldin et al (2014) suggest fitting flexible multivariate models to the rotated returns using the VT approach. Second, the symmetric square root rotation of Noureldin et al (2014) is not the most general type of rotation one could use-see, for instance, the hyper-rotation suggested by Asai and McAleer (2020) and the structural multivariate GARCH approach of Hafner et al (2020). Both use generalized rotations that are not necessarily symmetric.…”

Goodness‐of‐fit tests for the multivariate Student‐t distribution based on i.i.d. data, and for GARCH observations

“…More recently however, models with time-varying volatility have been employed in finance, with prime examples being several versions of generalized autoregressive conditional heteroskedasticity (GARCH) models with increasing flexibility, and in this regard applications of StDs with such models are numerous; for reviews of multivariate GARCH models the reader is referred to Bauwens et al (2006), Tsay (2006), Silvennoinen and Teräsvirta (2009), and Boudt et al (2019). In most of these reviews as well as in many other studies, the multivariate StD is consistently suggested as innovation distribution; see for instance, Harvey et al (1992), Pesaran and Pesaran (2007), Santos et al (2013), Rossi and Spazzini (2010), Diamantopoulos and Vrontos (2010), Creal et al (2011), Wang and Tsay (2013), Asai and So (2015), Dube et al (2016), Zheng et al (2018), Chib and Zeng (2020), Chen and Gerlach (2021) and Hafner et al (2020), among others.…”