On diagnostics in conditionally heteroskedastic time series models under elliptical distributions

In statistical diagnostics and sensitivity analysis, the local influence method plays an important role. In the present paper, we use this method to study financial time series data and conditionally heteroskedastic models under elliptical distributions. We start with a likelihood displacement, and consider data- and model-perturbation schemes. We obtain corresponding matrices of derivatives, and measures of slope and normal curvature, and then discuss the assessment of local influence.