An increasingly valuable tool for modelling a nonstationary time series, X(t), is time deformation. In this procedure time, t, is transformed to a 'time' scale, u = g(t), on which the process Y(u) = X(g(t)) is stationary. However, since the time scale is transformed, equally spaced data on the...

This paper introduces discrete Euler processes and shows their application in detecting and forecasting cycles in non-stationary data where periodic behavior changes approximately linearly in time. A discrete Euler process becomes a classical stationary process if 'time' is transformed properly....