This paper describes the application of high-confidence-interval prediction methods to the aircraft trajectory prediction problem, more specifically to the altitude prediction during climb. We are interested in methods for finding two-sided intervals that contain, with a specified confidence, at least a desired proportion of the conditional distribution of the response variable. This paper introduces two-sided Bonferroni-quantile confidence intervals, which is a new method for obtaining high-confidence two-sided intervals in quantile regression. This paper also uses the Bonferroni inequality to propose a new method for obtaining tolerance intervals in least squares regression. The latter has the advantages of being reliable, fast, and easy to calculate. We compare physical point-mass models to the introduced models on an air traffic management data set composed of traffic at major French airports. Experimental results show that the proposed interval prediction models perform significantly better than the conventional point-mass model currently used in most trajectory predictors. When comparing with a recent state-of-the-art point-mass model with adaptive mass estimation, the proposed methods give altitude intervals that are slightly wider but more reliable.
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