The New Prediction Method for Discrete Observations Based on Taylor’s Formula

摘要

Prediction is an important problem in many fields. For the prediction of a given variable with a sequence of observations, we propose a new method based on the use of Taylor's formula. The method can besummarized as follows：Firstly, for a sequence of discrete observations which may contain noise, we usetracking-differentiators to filter the noise or smooth the observation results, and obtain the estimation of theirdifferential values. Secondly, for the prediction, we use Taylor's formula to predict the future evolution of theobservations. Theoretical estimation is provided to guarantee the precision of the relevant prediction results.And simulation results for certain kinds of observations indicate the effectiveness of the method.