Title: Misspecification tests in conditional covariances for large cross-sectional dimensions
Authors: Bilel Sanhaji - Paris VIII (France) [presenting]
Thomas Chuffart - Besancon (France)
Abstract: Lagrange multiplier tests for nonlinearity in conditional covariances in multivariate GARCH models are proposed. The null hypothesis is the full BEKK model with variance targeting in which covolatilities of time series are driven by a linear function of their own lags and lagged squared innovations. The alternative hypothesis is an extension of the model in which covolatilities are modeled by a nonlinear function of the lagged squared innovations, represented by an exponential or a logistic transition function. Partial tests are also introduced in order to determine whether the relationship of time series or group of time series is linear or nonlinear. We investigate the size and power of these tests through Monte Carlo experiments, and we provide empirical illustrations in many of which cases these tests encourage the use of nonlinearity in conditional covariances.