In this paper, we focus on the building of an invariant distribution function associated to a non-stationary sample. After discussing some specific problems encountered by non-stationarity inside samples like the "spurious" long memory effect, we build a sequence of stationary processes...

The dynamic dependencies in financial market volatility are generally well described by a long-memory fractionally integrated process. At the same time, the volatility risk premium, defined as the difference between the ex-post realized volatility and the market’s ex-ante expectation thereof,...