Statistical results on autoregressive conditionally heteroscedastic models

The aim of this paper is to present some statistical aspects of an order 1 autoregressive model with errors following a stationary and ergodic generalised threshold ARCH process. So, to analyse the precision of forecasts obtained with these models a probabilistic study will be done. Moreover, a consistent test for a general AR (1) model with errors following an ergodic white noise of null conditional median will be developed and applied to our stochastic processesAvailable from Departamento de Matematica, Universidade de Coimbra, 3000 Coimbra, Portugal / FCT - Fundação para o Ciência e a TecnologiaSIGLEPTPortuga