  The influence of the past price behaviour on the realized volatility is
investigated in the present article. The results show that trending (drifting)
prices lead to increased (decreased) realized volatility. This ``volatility
induced by trend'' constitutes a new stylized fact. The past price behaviour is
measured by a product of 2 non overlapping returns, of the form r L[r] where L
is the lag operator. The effect is studied empirically using USD/CHF foreign
exchange data, in a large range of time horizons. A set of ARCH based processes
are modified in order to include the trend effect, and their forecasting
performances are compared. For a better forecast, it is shown that the main
factor is the shape of the memory kernel (i.e. power law), and the following
factor is the inclusion of the trend effect.
