Marked empirical processes for non-stationary time series

Ngai Hang Chan, Rongmao Zhang

Consider a first-order autoregressive process $X_i=\beta X_{i-1}+{\epsilon }_i,$ where ${\epsilon }_i=G({\eta }_i,{\eta }_{i-1},\dots )$ and ${\eta }_i,i\in \mathbb{Z}$ are i.i.d. random variables. Motiva…