CN105844347A - Individual stock index prediction method based on Lagrange multiplier method - Google Patents

Abstract

An embodiment of the invention discloses an individual stock index prediction method based on a Lagrange multiplier method. The method comprises the following steps of recording historical data of a highest point, a lowest point, an opening quotation point and a closing quotation point of an individual stock index in the past period of working days; using the Lagrange multiplier method to carry out fitting on all the historical data average trends; constructing a Lagrange function, determining to fit a triple-order polynomial and each coefficient and marking a fitted curve stationary point; extending a fitting curve so as to classify a subsequent trend; and according to different classifications and trend changes, predicting a subsequent stock index. In the embodiment of the invention, during individual stock index prediction, a triple-order polynomial function is used to carry out fitting; during a fitting process, the historical data of the opening quotation point, the closing quotation point, the highest point and the lowest point of an individual stock is used so that a prediction trend and a fluctuation interval are provided for a user, and high operation efficiency is possessed.

Description

A kind of method of single prediction of stock indices based on lagrange's method of multipliers

Technical field

The present invention relates to field of computer technology, especially relate to a kind of single stock index based on lagrange's method of multipliers pre- The method surveyed.

Background technology

China Stock Markets, through the development of nearly 20 years and perfect, have been achieved with huge achievement.It is known that stock has Still there is great risk however stock market has still attracted the participation of countless stock invester the highest return rate.But stock The people can be uneven to the analysis of stock, how to reduce risk by reasonable prediction analysis, seeks maximum benefit, become and seek Look for the emphasis in the prediction of reasonable stock index method.

Prediction of stock indices occupies critical role in equity investment field, although there being a variety of software for analysing stock, But the major function collection of current the type software provides real-time market to update with information data, and for stock for intelligence Deficiency in the exploitation of energy analysis decision.And stock index conversion amplitude is big in practice, changing factor is many, and change instability can be right How user selects stock to cause tremendous influence.

At present, a lot of stock index forecasting methods are all based on the Forecasting Methodology of neutral net, and this method just has preferably Network structure, but variable chooses difficulty, and influence factor is numerous, and pace of learning is slow, so it is automatic to realize this kind of algorithm with machine Change operation stock exchange and there is the least difficulty.But major part user wish to find a kind of can intellectual analysis and the prediction of decision-making How method, find one reasonable prediction stock index can be prone to again computer implemented Forecasting Methodology with needs.

Summary of the invention

A kind of method that it is an object of the invention to provide single prediction of stock indices based on lagrange's method of multipliers, energy Enough reach to predict the purpose that single stock index changes.

In order to solve the problems referred to above, the present invention proposes a kind of single prediction of stock indices based on lagrange's method of multipliers Method, including:

To the peak of single stock index in one period of working day of past, minimum point, opening quotation point, the history number of closing quotation point According to carrying out record；

Utilize lagrange's method of multipliers that all historical data average tendency are fitted；

Structure Lagrangian determines the curve stationary point after matching three rank multinomial and each term coefficient labelling matching；

Extend matched curve follow-up trend is classified；

According to different classification and Long-term change trend, follow-up stock index is predicted.

Described to going through that the peak of single stock index in one period of working day of past, minimum point, opening quotation point, closing quotation are put History data carry out record and include:

(x_j,y_i), i=j=1,2,3...80

Wherein x_jRepresent time, y_iRepresenting single stock index, i, j represent one section respectively and workaday always count, and totally eight ten Individual point.

Curve after described structure Lagrangian determines matching three rank multinomial and each term coefficient labelling matching is stayed Point includes:

Choosing three rank polynomial fitting types is:

Y=f (x, a₀,a₁,a₂,a₃)=a₀+a₁x+a₂x²+a₃x³+e

Wherein a₀,a₁,a₂,a₃Representing the three each term coefficient of rank polynomial fitting, x represents single stock index, and y represents the time, Variable e is the error between the actual function of fitting function and single stock index.

Described structure cubic polynomial is about the Lagrangian of error sum of squares e:

$e=\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}{\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]}^2$

Wherein: a₀,a₁,a₂,a₃Represent the three each term coefficient of rank polynomial fitting, y_iRepresent single stock index, x_jWhen representing Between, variable e is the error between the actual function of fitting function and single stock index, and i represented in one period of working day in the past Measuring point sum, totally eight ten points, k represents Mon-Fri measuring point sum.

Described method also includes:

Make described error sum of squares minimum so that it is determined that matching three rank multinomial and each term coefficient and most preferably approach its calculating Process is:

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_0}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_1}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_2}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k^2=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_3}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k^3=0;$

Try to achieve the expression formula of optimal three rank approximation by polynomi-als under lagrange's method of multipliers:

Y=a₀+a₁x+a₂x²+a₃x³

WhereinRepresent respectively to a₀,a₁,a₂,a₃Ask partial derivative, a₀,a₁,a₂,a₃Represent three rank polynomial fittings every Coefficient, y_iRepresent single stock index, x_jRepresenting the time, variable e is between the actual function of fitting function and single stock index Error, i represents the measuring point sum in the past one period of working day, and totally eight ten points, it is total that k represents Mon-Fri measuring point Number.

Described method also includes:

Analyze three rank polynomial curves after matching, make respectively

$\frac{dy}{dx}=0,\frac{d^{2}y}{d^{2}x}=0$

Wherein y represents single stock index, and x represents the time,Represent the three polynomial first derivatives in rank,Represent The three polynomial second dervatives in rank；

Calculate three polynomial fitting curve stationary point, rank and extreme points, bent to three rank multinomials with extreme point situation according to stationary point Line trend is categorized as rising, declines, maintain an equal level three kinds of trend, according to different classification and Long-term change trend to follow-up single stock index It is predicted.

By implementing the embodiment of the present invention, intend single prediction of stock indices have employed three rank polynomial functions Close, fit procedure make use of the opening quotation point of single stock, point of closing, peak, the historical data of minimum point, it is possible to for user Provide anticipation trend and waving interval, and there is the highest operation efficiency.Can be user by three rank fitting of a polynomials There is provided the trend prediction that single stock changes, it is also possible to provide interval to the peak of single stock with the fluctuation range of minimum point Prediction.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing In having technology to describe, the required accompanying drawing used is briefly described, it should be apparent that, the accompanying drawing in describing below is only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to Other accompanying drawing is obtained according to these accompanying drawings.

Fig. 1 is the method flow of based on lagrange's method of multipliers the single prediction of stock indices in the embodiment of the present invention Figure；

Fig. 2 is stock certificate data schematic diagram in the use three rank fitting of a polynomial surrounding in the embodiment of the present invention；

Fig. 3 is the three rank multinomials that the prediction next day of trade single stock index in the embodiment of the present invention rises situation Functional image；

Fig. 4 is the three rank polynomial functions that the prediction next day of trade stock index in the embodiment of the present invention declines situation Image；

Fig. 5 is that the wherein red curve in the embodiment of the present invention represents the next one day of trade various feelings of single stock index Most preferably approaching of condition.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Describe, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiments wholely.Based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under not making creative work premise Embodiment, broadly falls into the scope of protection of the invention.

Lagrange's method of multipliers is to solve the important method in mathematical optimization problem, by the function of many variables at arbitrary finite or The one-to-one relationship between extreme point and Lagrangian extreme point under multiple constraintss, thus find Lagrange Function Extreme Value point the most just have found function of many variables extreme point under these constraintss.

The character that the single stock index of the present invention is relevant to historical data factor, structure Lagrangian is given about going through Most preferably approaching of history data, by most preferably approaching the subsequent prediction providing single stock index.

The present invention asks conditional extremum structure convenient lagrange's method of multipliers, and machine realizes easy feature and utilizes with single Prediction of stock indices field, by the pass series structure Lagrange of three rank multinomials with error sum of squares e during matching historical data Function, and curve after matching is analyzed, the present invention is capable of the prediction to single stock index.

Fig. 1 is the method flow diagram of based on lagrange's method of multipliers the single prediction of stock indices in present example, The present invention to implement step as follows；

Mon-Fri stock index curve generalization historical data in S101, record surrounding；

From past surrounding from the Mon-Fri peak of label stock index day by day, minimum point, opening quotation point, closing quotation Point, totally eight ten measuring points are recordable is

(x_j,y_i), i=j=1,2,3...80

Wherein x_jRepresent time, y_iRepresent stock index.

S102, utilize lagrange's method of multipliers that all historical data general trends are fitted；

Choosing three rank polynomial fitting types is:

Y=f (x, a₀,a₁,a₂,a₃)=a₀+a₁x+a₂x²+a₃x³+e

Wherein e is error sum of squares.

S103, determine the curve stationary point after matching three rank multinomial and each term coefficient labelling matching；

Structure cubic polynomial and the Lagrangian of error sum of squares e:

$e=\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}{\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]}^2$

Make described error sum of squares minimum so that it is determined that matching three rank multinomial and each term coefficient and most preferably approach its calculating Process seeks partial derivative for term coefficient each to multinomial:

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_0}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_1}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_2}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k^2=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_3}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\Σ}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k^3=0;$

Above equation is expressed as matrix form can obtain:

$\left[\begin{array}{cccc}80& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^2& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^3\\ \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^2& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^3& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^4\\ \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^2& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^3& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^4& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^5\\ \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^3& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^4& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^5& \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{x}_k^6\end{array}\right]\left[\begin{array}{c}{a}_0\\ a_1\\ a_2\\ a_3\end{array}\right]=\left[\begin{array}{c}\underset{i=1}{\overset{80}{\mathrm{\Σ}}}{y}_i\\ \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{y}_i{x}_k\\ \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{y}_i{x}_k^2\\ \underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{y}_i{x}_k^3\end{array}\right]$

Thus can obtain three each term coefficient a of rank multinomial₀,a₁,a₂,a₃。

S104, extend matched curve be categorized as follow-up trend rising, decline, fair three kinds of trend；

Three polynomial fitting curve stationary point, rank and extreme points are calculated according to first derivative and second dervative.According to stationary point and pole Three rank polynomial curve trend are categorized as rising, decline by value point situation, maintain an equal level three kinds of trend.Computing formula is:

$\frac{dy}{dx}=3a_3{x}^2+2a_{2}x+a_1=0;$

$\frac{d^{2}y}{d^{2}x}=6a_{3}x+2a_2=0;$

S105, according to different classification and Long-term change trend, follow-up stock index is predicted；

According to the three possible situations of the rank follow-up exponential trend of multinomial stock after matching, as shown in Figures 2 to 5, Fig. 2 is this Stock certificate data schematic diagram in the fitting of a polynomial surrounding of bright use three rank, wherein Fig. 3 refers to for the prediction next day of trade single stock Three rank polynomial function images of number rising situation, Fig. 4 is that three rank of prediction next day of trade stock index decline situation are many Item formula functional image, Fig. 5 is that wherein red curve represents most preferably forcing the next day of trade various situation of single stock index Closely.

To sum up, the present invention is fitted have employed three rank polynomial functions in single prediction of stock indices, fit procedure In make use of the opening quotation point of single stock, point of closing, peak, the historical data of minimum point, it is possible to provided the user prediction Trend and waving interval, and there is the highest operation efficiency.Single stock can be provided the user by three rank fitting of a polynomials The trend prediction of ticket change, it is also possible to provide interval prediction with the fluctuation range of minimum point to the peak of single stock.

One of ordinary skill in the art will appreciate that all or part of step in the various methods of above-described embodiment is can Completing instructing relevant hardware by program, this program can be stored in a computer-readable recording medium, storage Medium may include that read only memory (ROM, Read Only Memory), random access memory (RAM, Random Access Memory), disk or CD etc..

It addition, above based on lagrange's method of multipliers the single prediction of stock indices that the embodiment of the present invention is provided Method is described in detail, and principle and the embodiment of the present invention are set forth by specific case used herein, with The explanation of upper embodiment is only intended to help to understand method and the core concept thereof of the present invention；General simultaneously for this area Technical staff, according to the thought of the present invention, the most all will change, in sum, This specification content should not be construed as limitation of the present invention.

Claims (6)

1. the method for a single prediction of stock indices based on lagrange's method of multipliers, it is characterised in that including:

The peak of single stock index in one period of working day of past, minimum point, opening quotation point, the historical data of closing quotation point are entered Row record；

Utilize lagrange's method of multipliers that all historical data average tendency are fitted；

Structure Lagrangian determines the curve stationary point after matching three rank multinomial and each term coefficient labelling matching；

Extend matched curve follow-up trend is classified；

According to different classification and Long-term change trend, follow-up stock index is predicted.

2. the method for single prediction of stock indices based on lagrange's method of multipliers as claimed in claim 1, it is characterised in that The described historical data putting the peak of single stock index in one period of working day of past, minimum point, opening quotation point, closing quotation is entered Row record includes:

(x_j,y_i), i=j=1,2,3...80；

Wherein x_jRepresent time, y_iRepresenting single stock index, i, j represent one section respectively and workaday always count, totally eight ten Point.

3. the method for single prediction of stock indices based on lagrange's method of multipliers as claimed in claim 2, it is characterised in that Curve stationary point after described structure Lagrangian determines matching three rank multinomial and each term coefficient labelling matching includes:

Choosing three rank polynomial fitting types is:

Y=f (x, a₀,a₁,a₂,a₃)=a₀+a₁x+a₂x²+a₃x³+e

Wherein a₀,a₁,a₂,a₃Representing the three each term coefficient of rank polynomial fitting, x represents single stock index, and y represents time, variable e For the error between the actual function of fitting function and single stock index.

4. the method for single prediction of stock indices based on lagrange's method of multipliers as claimed in claim 3, it is characterised in that Described structure cubic polynomial is about the Lagrangian of error sum of squares e:

$e=\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}{\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]}^2$

Wherein: a₀,a₁,a₂,a₃Represent the three each term coefficient of rank polynomial fitting, y_iRepresent single stock index, x_jRepresent the time, become Amount e is the error between the actual function of fitting function and single stock index, and i represents the measuring point in one period of working day in the past Sum, totally eight ten points, k represents Mon-Fri measuring point sum.

5. the method for single prediction of stock indices based on lagrange's method of multipliers as claimed in claim 4, it is characterised in that Described method also includes:

Make described error sum of squares minimum so that it is determined that matching three rank multinomial and each term coefficient and most preferably approach its calculating process For:

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_0}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_1}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_2}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k^2=0;$

$\frac{\mathrm{\δ}e}{{\mathrm{\δa}}_3}=2\underset{i=1,k=i\mathrm{mod}20}{\overset{80}{\mathrm{\Σ}}}\[y_i-(a_0+a_1{x}_k+a_2{x}_k^2+a_3{x}_k^3)\]x_k^3=0;$

Try to achieve the expression formula of optimal three rank approximation by polynomi-als under lagrange's method of multipliers:

Y=a₀+a₁x+a₂x²+a₃x³

WhereinRepresent respectively to a₀,a₁,a₂,a₃Ask partial derivative, a₀,a₁,a₂,a₃Represent the three each term coefficient of rank polynomial fitting, y_iRepresent single stock index, x_jRepresenting the time, variable e is the mistake between the actual function of fitting function and single stock index Difference, i represents the measuring point sum in one period of working day in the past, totally eight ten points, and k represents Mon-Fri measuring point sum.

The method of based on lagrange's method of multipliers single prediction of stock indices the most as claimed in claim, it is characterised in that Described method also includes:

Analyze three rank polynomial curves after matching, make respectively

$\frac{dy}{dx}=0,\frac{d^{2}y}{d^{2}x}=0$

Wherein y represents single stock index, and x represents the time,Represent the three polynomial first derivatives in rank,Represent three rank many The second dervative of item formula；

Calculate three polynomial fitting curve stationary point, rank and extreme points, with extreme point situation, three rank polynomial curves are become according to stationary point Gesture is categorized as rising, declines, maintain an equal level three kinds of trend, carries out follow-up single stock index according to different classification and Long-term change trend Prediction.