Gray model (GM) (1,1) prediction method of orthogonal interpolation based on Markov chain

Abstract

The invention discloses a gray model (GM) (1,1) prediction method of orthogonal interpolation based on Markov chain. According to the grey orthogonal method and the principle of the Markov chain, the Gauss-Chebyshev orthogonal thought is used to predict overall trend of time-series data. Accuracy of the prediction is time-varying, the principle of the Markov chain has good advantages during the process of processing a time-varying system, and choosing the GM (1,1) prediction method of the orthogonal interpolation based on the Markov chain can solve the instability of the prediction result better, and therefore the grey Markov orthogonal model is put forward for the prediction of data of electricity consumption, and is suitable for a dynamic prediction process which is of a short-middle term, low in demanded quantity of data and large in data amplitude. The GM (1,1) prediction method of the orthogonal interpolation based on the Markov chain is scientific in inventive concept, simple to calculate, small in work load, and high in prediction accuracy, and good in usage value and wide in application range in the technical field of prediction.

Description

technical field [0001] The invention relates to the field of data prediction methods, in particular to a GM(1,1) model prediction method based on Markov chain orthogonal interpolation. 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 equati...

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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

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