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arXiv · 2005.09145

Bootstrap prediction intervals with asymptotic conditional validity and unconditional guarantees

Yunyi Zhang·Dimitris N. Politis
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Abstract

It can be argued that optimal prediction should take into account all available data. Therefore, to evaluate a prediction interval's performance one should employ conditional coverage probability, conditioning on all available observations. Focusing on a linear model, we derive the asymptotic distribution of the difference between the conditional coverage probability of a nominal prediction interval and the conditional coverage probability of a prediction interval obtained via a residual-based bootstrap. Applying this result, we show that a prediction interval generated by the residual-based bootstrap has approximately 50% probability to yield conditional under-coverage. We then develop a new bootstrap algorithm that generates a prediction interval that asymptotically controls both the conditional coverage probability as well as the possibility of conditional under-coverage. We complement the asymptotic results with several finite-sample simulations.

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BibTeXRIS

Yunyi Zhang, Dimitris N. Politis. 2020-05-19. Bootstrap prediction intervals with asymptotic conditional validity and unconditional guarantees. https://arxiv.org/abs/2005.09145

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