Bootstrap

We construct bootstrap prediction intervals in the multi-step ahead prediction problem with parametric model estimator; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive—as opposed to fitted—residuals in the bootstrap process.

We consider a forward bootstrap approach with non-parametric model estimator to resolve the difficulty on predicting multi-step ahead time series data. We construct a quantile prediction interval that is asymptotically valid. Moreover, after taking a debiasing technique, we can build pertinent prediction intervals in which the estimation variability is captured. (This is my first paper with my advisor Professor Politis. Thanks for his guidance!)