Research On Forecasting Theory And Method Based On Data Analysis

The purpose of forecasting is providing the necessary future information fordecision-making system. In the dynamic technology fields of modern society, when peopledevelop a new technology or design a new product, it is hard to be success if people do not seekdevelopment trend or do not make prediction or prejudge. Therefore, it is no exaggeration to say,without prediction or prejudge, there is no scientific decision-making and there will be not existthe rapid development of science, technology and economic.During recent several decades, although the extensive research of traditional forecastingtheory and methods have made much more progress; there is still a considerably big gap betweenthe forecasting theoretical results and the requirement of practical application due to thecomplexity and variety of environment. This dissertation starts with the concrete problems thatlarge-scale data trend analysis may encounter while people use the existing forecasting methodsto make practical trends prediction, and makes further extensive study on the traditionalforecasting theory and methods from different aspects. The details are given as follows.1. Extensions for GM(1,1) formula by numerical approximation theory.GM(1,1) formula is an important research results in the gray prediction theory. The startingpoint of the study is to predict the future development trend of the things under the conditions of“less data”,“insufficient information”. However, from the general sense, for any time series,there will exist the phenomenon of inaccurate forecasts or the prediction accuracy can not reachthe required standards when this kind of fitting method that we used do not suitable for thechange rule of the time series data. Therefore, it is quite necessary to make correspondingimprovement for GM(1,1) forecast model. Based on the profound understanding of theconstruction regular of GM(1,1) model, this paper concluded the reasons which influence theprediction accuracy to three index:(1) selection of initial conditions;(2) reconstruction of thebackground value;(3) improvement of parameter estimation method. One index (2), that is, thereconstruction of the background value, has very important sense, because, according to theiterative nature of GM(1,1) model, index (1) and (3) will eventually attributed to thereconstruction of the background value, therefore, the construction method of background valuewill directly influence the prediction precision and applicability of GM(1,1) model.Based on the above analysis, this paper takes the background reconstruction as the researchfocus in the first part of this paper (Chapter3), the main task was realized by related methods innumerical approximation theory. The specific research programs include: improve the structuralform of background value by using piecewise linear Lagrange interpolation method and piecewise linear Newton interpolation method; improve the structural form of background valueby using cubic spline function; improve the structural form of background value by using Gaussinterpolation formula; make a second amendment of the forecasting results of Gauss-Chebyshevorthogonal prediction model by using Markov chain principle. Among them, the first typeprogram focus on the convergence and stability of the numerical solution of background value;the second type program focus on the smoothness of numerical solution of background value; thethird type program focus on the algebraic precision of background value; the fourth type programfocus on the amendment process when the background value was restructured by the numericalmethods2. The Extensive research for semi-parametric regression prediction model.This paper focuses on the semi-parametric statistical model for the trend forecast of certaindata and uncertain data. As a typical model, the semi-parametric statistical model has bothparameters component and non-parameters component, it focuses on the main part (ie. theparameters component), and without losing the effect of the distracters (ie. the non-parameterscomponent). On the one hand, this kind of statistical model solves the difficult problem that pureparameter model and non-parameter model difficult to face, enhances the applicability of thesemi-parameter regression model, on the other hand, it can overcome the defect that informationlosing excessive when utilizes the non-parameter method, takes full advantage of the effectiveinformation provided by the data and obtains a high level of information extraction accuracy.Based on the above analysis, the specific solutions are as follows: Penalized least squaresmethod is introduced in the second part of this paper (Chapter4), It effectively solves theproblem that the number of unknown parameters are more than the number of equations, and thisproblem can lead the solution of minimum value question V TPV minnot unique. Meanwhile,this paper introduces a smooth factor, provide a guarantee for smoothness estimates of thesolution curve, the reliability of semi-parametric prediction model has been greatly improved.Secondly, estimates the non-parametric part in the semi-parametric regression model by usingmoving average estimation ARMA method, put the traditional theoretical estimation formulafurther extended to the practical form, give an idea of the combined use of time series forecastingand statistical forecasting. Finally, estimate the distribution fitting function by makingdistribution fitting test on student residuals of the parameters part, take advantage of this fittingfunction approximately replace the unknown function of semi-parametric regression model, andconstruct a new semi-parametric regression model based on measure correction of residualdistribution. This model overcomes the influence of the residual interference, can automaticallyadjust the boundary effect, extends the research idea of semi-parametric regression model andimproves the accuracy of the semi-parametric regression forecasting model. Further more, considered the interval aggregation nature of the sample points in large sample, redefine the timegranularity, set information aggregation interval by utilizing differential element method,construct another new semi-parametric regression model based on variable interval weights andgives the corresponding solution algorithm.3. The traditional forecasting models are further extended after the introduction ofintelligent optimization methods.Two kinds of intelligent optimization methods are introduced in the third part of this paper(Chapter5):①Determine the autoregressive order p and moving average order q of ARMA(p,q)model by using adaptive genetic algorithm, improve the fitness function of genetic algorithm, byadjusting the parameters and evolved generation by generation, obtain the optimal ARMA model.②Improve the structural form of background value by building a particle swarm optimizationwith compression factor K, promote the research thinking of the traditional grey predictionmethod, on this basis, put the particle swarm optimization further extended to the case ofadaptive adjust inertia weight, and gives the corresponding solution algorithm.The extensive research results presented above not only enrich the content of forecastingtheory but also widen the applied areas of the traditional forecasting models, put forward newthinking for the study on the prediction method of data driven, and provide more sufficientscientific evidence for decision makers making decision which based on prediction information.