  The ability to know in advance the trend of running process instances, with
respect to different features, such as the expected completion time, would
allow business managers to timely counteract to undesired situations, in order
to prevent losses. Therefore, the ability to accurately predict future features
of running business process instances would be a very helpful aid when managing
processes, especially under service level agreement constraints. However,
making such accurate forecasts is not easy: many factors may influence the
predicted features.
  Many approaches have been proposed to cope with this problem but all of them
assume that the underling process is stationary. However, in real cases this
assumption is not always true. In this work we present new methods for
predicting the remaining time of running cases. In particular we propose a
method, assuming process stationarity, which outperforms the state-of-the-art
and two other methods which are able to make predictions even with
non-stationary processes. We also describe an approach able to predict the full
sequence of activities that a running case is going to take. All these methods
are extensively evaluated on two real case studies.
