A forecasting model based on high-frequency market makers' quotes of f
inancial instruments is presented. The statistical behaviour of these
time series leads to discussion of the appropriate time scale for fore
casting. We introduce variable time scales in a general way and define
the new concept of intrinsic time. The latter reflects better the act
ual trading activity. Changing time scale means forecasting in two ste
ps, first an intrinsic time forecast against physical time, then a pri
ce forecast against intrinsic time. The forecasting model consists, fo
r both steps, of a linear combination of non-linear price-based indica
tors. The indicator weights are continuously re-optimized through a mo
dified linear regression on a moving sample of past prices. The out-of
-sample performance of this algorithm is reported on a set of importan
t FX rates and interest rates over many years. It is remarkably consis
tent. Results for short horizons as well as techniques to measure this
performance are discussed.