Prediction Intervals: A Geometric View

This article provides a review of the approaches to the construction of prediction intervals. To increase the reliability of prediction, point prediction methods are replaced by intervals for many aims. The interval prediction generates a pair as future values, including the upper and lower bounds for each prediction point. That is, according to historical data, which include a graph of a continuous and discrete function, two functions will be obtained as a prediction, i.e., the upper and lower bounds of estimation. In this case, the prediction boundaries should provide guaranteed probability of the location of the true values inside the boundaries found. The task of building a model from a time series is, by its very nature, incorrect. This means that there is an infinite set of equations whose solution is close to the time series for machine learning. In the case of interval use, the inverse problem of dynamics allows us to choose from the entire range of modeling methods, using confidence intervals as solutions, or intervals of a given width, or those chosen as a solution to the problems of multi-criteria optimization of the criteria for evaluating interval solutions. This article considers a geometric view of the prediction intervals and a new approach is given.