Abstract We propose two Lagrange multiplier tests for nonlinearity in conditional covariances in multivariate GARCH models. The null hypothesis is the scalar BEKK model 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. Moreover, on the same basis we develop two other tests that are robust to leverage effects. 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.

中文翻译：

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条件协方差中的非线性检验

摘要针对多元GARCH模型中条件协方差的非线性，我们提出了两个Lagrange乘数检验。零假设是标量BEKK模型，在该模型中，时间序列的方差由其自身滞后和滞后平方创新的线性函数驱动。备选假设是模型的扩展，其中，通过滞后平方创新的非线性函数对协方差建模，该非线性函数由指数或逻辑对数转换函数表示。此外，在相同的基础上，我们还开发了另外两个可以充分利用效果的测试。我们通过蒙特卡洛实验研究了这些检验的大小和功效，并在许多情况下提供了经验说明，这些检验鼓励在条件协方差中使用非线性。