The conditions for strict stationary of power-GARCH processes whose innovations were described by a heavily-tailed and possibly asymmetric stable Paretian distribution were presented. The stationary conditions and forecasting performance of asymmetric power GARCH models with generalized Student's t distributions were examined. The empirical comparisons between S α,β,δGARCH and Student's t-GARCH models with value-at risk applications given in Mittnik and Paolella were also presented. The model was found to be capable of capturing the important features that characterized time series of returns on financial assets.
- Conditional heteroscedasticity
- Financial modeling
- Heavy tails
- Integrated GARCH
- State space representation