Statistical Inference for stable asymmetric GARCH models

Heavy-tailed phenomena are ubiquitous in the real world and are often observed in various scientific fields. However, the statistical inference for GARCH models in the heavy-tailed setting is either cumbersome or scarce of theoretical support. This paper develops a comprehensive statistical inference framework for an asymmetric generalized autoregressive conditional heteroskedasticity model with standardized non-Gaussian symmetric α-stable innovation (sAGARCH) within a unified framework of stationary and explosive cases. The paper first considers the maximum likelihood estimation of the model with its asymptotics, including estimation of the stable exponent parameter in the innovation. A modified Kolmogorov-type test statistic is then proposed for diagnostic checking, along with test statistics for assessing strict stationarity and asymmetry. Monte Carlo simulation studies are conducted to examine the finite-sample performance of our entire inference procedure, and empirical examples of stock return series are analyzed to illustrate the utility and validity of sAGARCH models in comparison to existing models in the literature.