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.