Portmanteau test for the asymmetric power GARCH model when the power is unknown

It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have incorporate so-called leverage effect. We derive asymptotic behaviour squared residuals autocovariances for class asymmetric power GARCH when unknown and jointly estimated with model’s parameters. then deduce a portmanteau adequacy test based on residuals. These results are illustrated by Monte Carlo experiments. An application real data also proposed.