Statistical Inference for time-varying ARCH processes

In this paper the class of ARCH infinity models is generalised to the nonstationary class of ARCH infinity models with time-varying coefficients. For fixed time points a stationary approximation is given leading to the notation `locally stationary ARCH infinity process'. The asymptotic properties of weighted quasi-likelihood estimates are studied including asymptotic normality. In particular the extra bias due to nonstationarity of the process is investigated. Moreover a Taylor expansion of the nonstationary ARCH process in terms of stationary processes is given and it is proved that the time-varying ARCH process can be written as a time-varying Volterra series.