GM (1, 1) model prediction method based on cubic spline

Abstract

The invention discloses a dynamic GM (1, 1) model based on a cubic spline interpolation. The dynamic GM (1, 1) model is applied for a thought of a piecewise polynomial interpolation and an overall trend of dynamic prediction time series data. The dynamic GM (1, 1) model based on the cubic spline interpolation theoretically analyzes a background value of a GM (1, 1) model. Firstly, a through of a cubic spline interpolation is put forward. Then, a method of combination of a piecewise linear interpolation function and a cubic spline interpolation formula to construct a new class grey prediction model. A constructing process of the background value can be improved so as to overcome the shortcomings of an existing grey improving model and provide a new means to improve prediction accuracy. Lastly, the model can be utilized to implement prediction. The dynamic GM (1, 1) model based on the cubic spline interpolation is scientific in concept, simple in calculation, small in workload and high in prediction accuracy. The dynamic GM (1, 1) model based on the cubic spline interpolation has a better use value and a wide application prospect in a prediction technique field.

Description

technical field [0001] The invention relates to the field of data prediction methods, in particular to a cubic spline-based GM (1,1) model prediction method. Background technique [0002] Gray theory is a mathematical method used to solve systems with incomplete information. This approach treats each random variable as a gray variable varying within a given range. Instead of using statistical methods to deal with gray variables, directly deal with the original data to find the internal law of change. Due to the large number of gray systems in many fields such as economics, social sciences and engineering, this forecasting method has been widely used. The basic idea of ​​the gray forecasting algorithm is: first, perform an accumulation operation on the original time series to generate a new time series; then, according to the gray theory, assuming that the new time series has an exponential change law, establish a corresponding differential equation for fitting, Then, disc...

AI Technical Summary

Problems solved by technology

[0009] Because when using the trapezoidal formula to obtain the approximate value of the definite integral as the background value, the error is usually large, which leads to a large deviation in the model prediction, and the prediction accuracy naturally fails to meet the requirements

However, through the research of the present invention, it is found that even if a more advanced interpolation algorithm is used to reconstruct the background value, there are certain limitations, because the previous studies all used a single interpolation method, although the model’s accuracy has been improved to a certain extent. Prediction accuracy, but there are also defects, that is, increasing the number of nodes for the one-sided pursuit of high precision leads to oscillations and distortion of predictions, resulting in reduced applicability or even unavailability of prediction models

Images