  The Model-free Prediction Principle of Politis (2015) has been successfully
applied to general regression problems, as well as problems involving
stationary time series. However, with long time series, e.g. annual temperature
measurements spanning over 100 years or daily financial returns spanning
several years, it may be unrealistic to assume stationarity throughout the span
of the dataset. In the paper at hand, we show how Model-free Prediction can be
applied to handle time series that are only locally stationary, i.e., they can
be assumed to be as stationary only over short time-windows. Surprisingly there
is little literature on point prediction for general locally stationary time
series even in model-based setups and there is no literature on the
construction of prediction intervals of locally stationary time series. We
attempt to fill this gap here as well. Both one-step-ahead point predictors and
prediction intervals are constructed, and the performance of model-free is
compared to model-based prediction using models that incorporate a trend and/or
heteroscedasticity. Both aspects of the paper, model-free and model-based, are
novel in the context of time-series that are locally (but not globally)
stationary. We also demonstrate the application of our Model-based and
Model-free prediction methods to speleothem climate data which exhibits local
stationarity and show that our best model-free point prediction results
outperform that obtained with the RAMPFIT algorithm previously used for
analysis of this data.
