Testing for volatility interactions in the Constant Conditional Correlation GARCH model

Abstract

In this paper, we propose a Lagrange multiplier test for volatility interactions among markets or assets. The null hypothesis is the Constant Conditional Correlation generalized autoregressive conditional heteroskedasticity (GARCH) model in which volatility of an asset is described only through lagged squared innovations and volatility of its own. The alternative hypothesis is an extension of that model in which volatility is modelled as a linear combination not only of its own lagged squared innovations and volatility but also of those in the other equations while keeping the conditional correlation structure constant. This configuration enables us to test for volatility transmissions among variables in the model. Monte Carlo experiments show that the proposed test has satisfactory finite-sample properties. The size distortions become negligible when the sample size reaches 2500. The test is applied to pairs of foreign exchange returns and individual stock returns. Results indicate that there seem to be volatility interactions in the pairs considered, and that significant interaction effects typically result from the lagged squared innovations of the other variables. Copyright The Author(s). Journal compilation Royal Economic Society 2009

Volatılıty Spıllovers from The Internatıonal Capıtal Inflows to Economıc Growth in Turkey

“…We compare the DCC-GARCH model to Constant Conditional Correlation GARCH model of Bollerslev (1990) using an Lagrange Multiplier (LM) test proposed by Nakatani and Terasvirta (2007). Finally, we find volatility spillovers in Turkish data from capital flows to economic growth.…”

A multivariate regime-switching GARCH model with an application to global stock market and real estate equity returns

“…It is an asymmetric multi-regime version of the extended CCC (ECCC) model studied by Jeantheau (1998), which itself generalizes the CCC of Bollerslev (1990) by allowing for volatility interactions, which are often of interest in finance and macroeconomics (e.g. Nakatani & Teräsvirta, 2009;andKaranasos 2010, 2015). In many applications the diagonal model, with all A j , B j , and j being diagonal matrices, will be preferred for reasons of parsimony; an ARCH version of such a model was used by Ramchand and Susmel (1998).…”

A Lagrange multiplier test for testing the adequacy of constant conditional correlation GARCH model

“…Their test is not restricted to conditional correlation GARCH models, but by a suitable choice of the conditional covariance matrix it becomes a misspeci…cation test of the GARCH equations in the CCC-GARCH model. Nakatani & Teräsvirta (2009) derived a test of the CCC-GARCH model against the Extended CCC-GARCH model of Jeantheau (1998). In their Lagrange multiplier (LM-) test the alternative to the GARCH equations is the model with GARCH equations that contains lags of squared errors and conditional variances from other GARCH equations.…”

“…In their Lagrange multiplier (LM-) test the alternative to the GARCH equations is the model with GARCH equations that contains lags of squared errors and conditional variances from other GARCH equations. Our aim is to derive a general portmanteau test in the spirit of Ling & Li (1997) such that the alternative to the GARCH equations is more general than in the test of Nakatani & Teräsvirta (2009). It is based on decomposing the conditional variance equations in the CCC-GARCH model multiplicatively into two components, one of which represents the null model, whereas the other one describes the misspeci…cation.…”