Predictive Inference for Locally Stationary Time Series

Abstract

The Model-free Prediction Principle of Politis (Test 22(2):183–250, 2013) has been successfully applied to both 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 modeled as stationary only over short time-windows. Both one-step-ahead point predictors and prediction intervals are constructed and compared.