Size and Power of Diagnostic Tests for Asymmetric Garch-Type Models

Generalized autoregressive conditional heteroscedasticity (GARCH)-type models have been successively used to capture the conditional volatility of macroeconomic and financial time series in the past two decades. However, few diagnostic tests are specifically devised to check the adequacy of symmetric multivariate GARCH specifications. Moreover, most practitioners resort to the popular Ljung-Box test indiscriminately, even though the appropriateness of such a test is questionable. In this paper, we investigate the empirical size and power of four diagnostic tests: the Ling-Li test, Ljung-Box test, the Box-Pierce test modified by Tse and Tsui, and the runs test, respectively. We use Monte Carlo simulation experiments over a wide combination of data generating processes and estimation models of bivariate GARCH-type asymmetric models. In the absence of analytically derived diagnostic tests, our simulation results could serve as guidelines for empirical researchers and practitioners in selecting the appropriate diagnostic tests for multivariate asymmetric GARCH models.