Bootstrap prediction intervals for power-transformed time series

Abstract

In this paper, we propose a bootstrap procedure to construct prediction intervals for future values of a variable after a linear ARIMA model has been fitted to its power transformation. The procedure is easy to implement and provides a useful tool in empirical applications given that it is often the case that, for example, the log-transformation is modeled when the variable of interest for prediction is the original one. The advantages over existing methods for computing prediction intervals of power-transformed time series are that the proposed bootstrap intervals incorporate the variability due to parameter estimation and do not rely on distributional assumptions neither on the original variable nor on the transformed one. We derive the asymptotic distribution and show the good behavior of the bootstrap approach versus alternative procedures by means of Monte Carlo experiments. Finally, the procedure is illustrated by analyzing three real-time series data sets.