Portmanteau test for the asymmetric power GARCH model when the power is unknown
This work addresses volatility modeling for financial returns, specifically incorporating the leverage effect, but it is incremental as it extends existing GARCH frameworks with a new test.
The authors tackled the problem of modeling daily financial returns by developing a portmanteau adequacy test for asymmetric power GARCH models with unknown power, deriving asymptotic results for squared residuals autocovariances and validating them through Monte Carlo experiments and real financial data applications.
It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have to incorporate the so-called leverage effect. We derive the asymptotic behaviour of the squared residuals autocovariances for the class of asymmetric power GARCH model when the power is unknown and is jointly estimated with the model's parameters. We then deduce a portmanteau adequacy test based on the autocovariances of the squared residuals. These asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed.