CN103399867B - A kind of self-adapting regulation method of linear combination prediction model weight - Google Patents

Abstract

The invention discloses a kind of self-adapting regulation method of linear combination prediction model weight, it is characterized in that: (1) weight w _i,mwith forecast model f _ithe m time outer before the result of calculation of k-1 time relevant to front k actual result related coefficient; (2) weight w _i,mwith forecast model f _ithe m time result of calculation relevant with the deviation of actual result, the forecast model less with nearest actual result deviation, arranges higher weight; (3) what calculate that (1) related coefficient of obtaining and calculating (2) obtains respectively predicts the outcome and the deviation of actual result, thus reaches the object calculating adaptive weighting.The present invention has fully taken into account and has predicted the outcome with the deviation of actual result and predict the outcome and the related coefficient of front k result in the weight self-adaptative adjustment of linear combination model calculates, and adds accuracy and the rationality of algorithm.

Description

A kind of self-adapting regulation method of linear combination prediction model weight

Technical field

The present invention relates to a kind of in tax index prediction, predicting the outcome and actual result according to linear combination forecasting model, dynamically changes the method for the weight of each forecast model.

Background technology

In combination linear prediction, each forecast model role in prediction is not changeless, but affects dynamic change by all kinds of extraneous factor.Such as, in tax index prediction, each forecast model is by the impact of macroeconomy situation, all kinds of economy and the tax policy.Because all kinds of factor is to the difference of forecast model influence degree, the weight of each forecast model, also in dynamic change, in order to ensure the performance of linear combination forecasting model, needs to carry out dynamic conditioning adaptively to it.Applicant is new through looking into, and retrieved one section of relevant patent: weight adjusting module and weight regulating method [application publication number: CN1925543].In that patent, inventor provides a kind of weight adjusting module and weight regulating method, is applicable to adjust the weight in image-zooming technology.It is all for embody rule that above-mentioned Patents invents described method, and algorithm idea and the self-adaptative adjustment Weight algorithm that this method adopts have essence different.

Summary of the invention

The object of this invention is to provide one can according to predicted value and actual result, dynamic alignment combination forecasting in i-th forecast model f _iweights omega _i(i ∈ [1..n]) carries out the method for accommodation.

For reaching above object, the present invention takes following technical scheme to be achieved:

A self-adapting regulation method for linear combination prediction model weight, is characterized in that, in accordance with the following steps:

(1) initial weight is determined: set the numerical value of actual result first as F ' ₀, each forecast model f _ipredicted value be F ' _i; For each i ∈ [1..n], calculate then each forecast model f _iinitial weight be meet the model that prediction effect is good first and there is higher initial weight, and

(2) dynamic conditioning weight:

A, establish current totally to predict the outcome for m time and actual result, comprise the F ' that predicts the outcome of before except the m time k-1 time _{i, m-k+1}, F ' _{i, m-k+2}.., F ' _{i, m-1}, and the actual result F ' of first k time _m-k+1,

F ' _m-k+2.., F ' _m; Wherein, k is time window, defaultly gets 5; As m < k, get k=m; Corresponding F ' _{i, m-k+1}, F ' _{i, m-k+2}.., F ' _{i, m-1}weight be respectively w _{i, m-k+1}, w _{i, m-k+2}.., w _{i, m-1};

B, forecast model f _i, i ∈ [1..n], the result of calculation of k-1 time and the related coefficient of front k actual result before except the m time;

C, forecast model f _ithe deviation of the m time result of calculation and actual result,

D, result according to A, B, self-adaptation solves each forecast model f _ithe weights omega of (i ∈ [1..n]) the m time adjustment _i,m, for the forecast model high and less with actual result deviation with actual result correlativity, increase the value of weight; For the forecast model low with actual result correlativity and the forecast model larger with actual result deviation, reduce the value of weight.

In such scheme, in described step (2), the specific algorithm of step B is:

STEP1. calculate $F_m={\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,m-1}{F}_{i,m}^{\&prime;};$

In order to avoid weight adjusting too frequently causes shake, as F ' _m=F _m=0 or | F ' _m-F _m|/(| F ' _m|+| F _m|)≤5%, do not carry out index weights adjustment, namely for each i ∈ [1..n], make ω _i,m=ω _{i, m-1}, return (ω _{1, m}, ω _{2, m}.., ω _i,m.., ω _n,m), algorithm exits;

STEP2. according to forecast model f _ithe result of calculation of (i ∈ [1..n]) and the related coefficient of actual result, determine weight adjusting coefficient:

STEP2.1. for each i ∈ [1..n], Pearson product-moment correlation coefficient (PPMCC) sequence of calculation F ' is adopted _{i, m-k+1}, F ' _{i, m-k+2}.., F ' _{i, m-1}with F ' _m-k+1, F ' _m-k+2.., F ' _m-1related coefficient, obtain one group of correlation coefficient r _i, r _i∈ [-1,1];

$r_i=\frac{{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}(F_{i,j}^{\&prime;}-{\stackrel{\&OverBar;}{F}}_i^{\&prime;})(F_j^{\&prime;}-{\stackrel{\&OverBar;}{F}}^{\&prime;})}{\sqrt{{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{(F_{i,j}^{\&prime;}-{\stackrel{\&OverBar;}{F}}_i^{\&prime;})}^2{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{(F_j^{\&prime;}-{\stackrel{\&OverBar;}{F}}^{\&prime;})}^2}}---\left(1\right)$

In formula (1), ${\stackrel{\&OverBar;}{F}}_i^{\&prime;}={\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{F}_{i,j}^{\&prime;}/(k-1),$ ${\stackrel{\&OverBar;}{F}}^{\&prime;}={\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{F}_j^{\&prime;}/(k-1);$

STEP2.2. to correlation coefficient r _i(i ∈ [1..n]) carries out following zero correction, obtains one group of weight adjusting coefficient r ' _i, r ' _ishow more greatly forecast model f _ihigher with actual result correlativity;

$r_i^{\&prime;}=\left|r_i\right|-{\mathrm{\&Sigma;}}_{i=1}^n\left|r_i\right|/n;---\left(2\right)$

In described step (2), the specific algorithm of step C is:

Computational prediction model f _i(i ∈ [1..n]) the m time result of calculation F ' _i,mwith actual result F ' _mdeviation Δ F _i:

$\mathrm{\&Delta;}\stackrel{\&OverBar;}{F}=\frac{{\mathrm{\&Sigma;}}_{i=1}^n|F_{i,m}^{\&prime;}-F_m^{\&prime;}|}{n};---\left(3\right)$

$\mathrm{\&Delta;}{F}_i=\mathrm{\&Delta;}\stackrel{\&OverBar;}{F}-|F_{i,m}^{\&prime;}-F_m^{\&prime;}|;---\left(4\right)$

Deviation Δ F _ilarger, show forecast model f _ithe m time forecasting accuracy high.

In described step (2), the specific algorithm of D step is:

STEP1. computational prediction model f _ithe weight adjusting value Δ ω of (i ∈ [1..n]) _i,m:

STEP1.1. to correlation coefficient r ' _i(i ∈ [1..n]) and deviation Δ F _ispan normalization:

$r_i^{\&prime;}=\left|r_i\right|-{\mathrm{\&Sigma;}}_{i=1}^n\left|r_i\right|/n(r_i^{\&prime;}\&Element;[-\mathrm{1,1}\left]\right);---\left(5\right)$

$\mathrm{\&Delta;}{F}_i^{\&prime;}=\frac{\mathrm{\&Delta;}{F}_i+\min \left(\mathrm{\&Delta;}{F}_i\right)}{\max \left(\mathrm{\&Delta;}{F}_i\right)-\min \left(\mathrm{\&Delta;}{F}_i\right)}(\mathrm{\&Delta;}{F}_i^{\&prime;}\&Element;[-\mathrm{1,1}\left]\right);---\left(6\right)$

STEP1.2. computational prediction model f _ithe weight adjusting value Δ ω of (i ∈ [1..n]) _i,m

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_{i,m}={\mathrm{\&omega;}}_{i,m-1}\frac{(p_1{r}_i^{\&prime;}+p_2\mathrm{\&Delta;}{F}_i^{\&prime;})-{\mathrm{\&Sigma;}}_{i=1}^n(p_1{r}_i^{\&prime;}+p_2\mathrm{\&Delta;}{F}_i^{\&prime;})/n}{{\mathrm{\&Sigma;}}_{i=1}^n(p_1{r}_i^{\&prime;}+p_2\mathrm{\&Delta;}{F}_i^{\&prime;})}---\left(7\right)$

In formula (7), p ₁and p ₂be respectively correlation coefficient r ' _i, deviation Δ F _iweight, wherein p ₁+ p ₂=1, p under default setting ₁=0.4p ₂=0.6;

STEP2. for each i ∈ [1..n], ω is calculated _i,m;

ω′ _i,m=ω _i,m-1+Δω _i,mi∈[1..n] (8)

${\mathrm{\&omega;}}_{i,m}=\frac{{\mathrm{\&omega;}}_{i,m}^{\&prime;}}{{\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,m}^{\&prime;}}---\left(9\right)$

Weight adjusting value Δ ω _i,mmeet return (ω _{1, m}, ω _{2, m}.., ω _i,m.., ω _n,m).

Advantage of the present invention is, make use of forecast model f _ithe m time outer before the result of calculation of k-1 time and front k actual result related coefficient and forecast model f _ithe m time result of calculation and the deviation of actual result add the accuracy rate and rationality that algorithm calculates.

Accompanying drawing explanation

Below in conjunction with the drawings and the specific embodiments, the present invention is described in further detail.

Fig. 1 the inventive method process flow diagram.

Embodiment

What the present invention adopted is predicting the outcome and actual result according to linear combination forecasting model, dynamically changes the method for the weight of each forecast model.

Research purpose: predicting the outcome and actual result according to linear combination forecasting model, dynamically changes the weight of each tax index model.

Research background: in combination linear prediction, each forecast model role in prediction is not changeless, but affects dynamic change by all kinds of extraneous factor.Such as, in tax index prediction, each forecast model is by the impact of macroeconomy situation, all kinds of economy and the tax policy.Because all kinds of factor is to the difference of forecast model influence degree, the weight of each forecast model, also in dynamic change, in order to ensure the performance of linear combination forecasting model, needs to carry out dynamic conditioning adaptively to it.

As shown in Figure 1, a kind of self-adapting regulation method of linear combination prediction model weight, comprise 6 steps, its idiographic flow is:

(1) be F ' according to the numerical value of actual result first ₀with each forecast model f _ipredicted value be F ' _i, for each i ∈ [1..n], calculate each forecast model f _iinitial weight w _{i, 0};

(2) in order to avoid weight adjusting too frequently causes shake, if F ' _m=Fm=0 or | F ' _m-F _m|/(| F ' _m|+| F _m|)≤5%, do not carry out index weights adjustment, make ω _i,m=ω _{i, m-1}, algorithm exits, otherwise performs (3).

(3) according to forecast model f _ithe result of calculation of (i ∈ [1..n]) and the related coefficient of actual result, determine weight adjusting coefficient:

(4) computational prediction model f _i(i ∈ [1..n]) the m time result of calculation F ' _i,mwith actual result F ' _mrelative deviation Δ F _i:

(5) computational prediction model f _ithe weight adjusting value Δ ω of (i ∈ [1..n]) _i,m;

(6) for each i ∈ [1..n], ω is calculated _{i, m}=ω _{i, m-1}+ Δ ω _i,m; Return (ω _{1, m}, ω _{2, m}.., ω _i,m.., ω _n,m), algorithm exits.

According to following detailed step:

(1) initial weight is determined: set the numerical value of actual result (actual value of tax index) first as F ' ₀, each forecast model f _ipredicted value be F ' _i; For each i ∈ [1..n], calculate ${\mathrm{\&omega;}}_{i,0}^{\&prime;}=1-\frac{|F_0^{\&prime;}-F_i^{\&prime;}|}{|F_0^{\&prime;}+F_i^{\&prime;}|+1},$ Then each forecast model f _iinitial weight be ${\mathrm{\&omega;}}_{i,0}=\frac{{\mathrm{\&omega;}}_{i,0}^{\&prime;}}{{\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,0}^{\&prime;}},$ Meet the model that prediction effect is good first and there is higher initial weight, and

(2) dynamic conditioning weight: establish current totally to predict the outcome for m time and actual result; For each i ∈ [1..n], according to forecast model f _ithe result of calculation of k-1 time and front k actual result related coefficient before except the m time, and forecast model f _ithe deviation of the m time result of calculation and actual result, solves each forecast model f _ithe weights omega of (i ∈ [1..n]) the m time adjustment _i,m; For the forecast model high and less with nearest actual result deviation with actual result correlativity in early stage, increase the value of weight; For the forecast model low with actual result correlativity and the forecast model larger with nearest actual result deviation, reduce the value of weight.

Described dynamic conditioning weight performs according to following algorithm:

Input:

A) forecast model f _i(i ∈ [1..n]) except the m time before k-1 time (k is time window, defaultly gets 5; As m < k, get k=m) result of calculation be F ' _{i, m-k+1}, R ' _{i, m-k+2}.., F ' _{i, m-1};

B) corresponding F ' _{i, m-k+1}, F ' _{i, m-k+2}.., F ' _{i, m-1}weight be respectively w _{i, m-k+1}, w _{i, m-k+2}.., w _{i, m-1};

C) the actual result F ' of first k time _m-k+1, F ' _m-k+2.., F ' _m;

Export: vector (ω _{1, m}, ω _{2, m}.., ω _i,m.., ω _n,m), ω _i,mfor forecast model f _ithe weight adjusting result of the m time;

Step is:

STEP1. calculate $F_m={\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,m-1}{F}_{i,m}^{\&prime;};$

In order to avoid weight adjusting too frequently causes shake, as F ' _m=F _m=0 or | F ' _m-F _m|/(| F ' _m|+| F _m|)≤5%, do not carry out index weights adjustment, namely for each i ∈ [1..n], make ω _i,m=ω _{i, m-1}, return (ω _{1, m}, ω _{2, m}.., ω _i,m.., ω _n,m), algorithm exits;

STEP2. according to forecast model f _ithe result of calculation of (i ∈ [1..n]) and the related coefficient of actual result, determine weight adjusting coefficient:

STEP2.1. for each i ∈ [1..n], Pearson product-moment correlation coefficient (PPMCC) sequence of calculation F ' is adopted _{i, m-k+1}, F ' _{i, m-k+2}.., F ' _{i, m-1}with F ' _m-k+1, F ' _m-k+2.., F ' _m-1related coefficient, obtain one group of correlation coefficient r _i, r _i∈ [-1,1];

$r_i=\frac{{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}(F_{i,j}^{\&prime;}-{\stackrel{\&OverBar;}{F}}_i^{\&prime;})(F_j^{\&prime;}-{\stackrel{\&OverBar;}{F}}^{\&prime;})}{\sqrt{{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{(F_{i,j}^{\&prime;}-{\stackrel{\&OverBar;}{F}}_i^{\&prime;})}^2{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{(F_j^{\&prime;}-{\stackrel{\&OverBar;}{F}}^{\&prime;})}^2}}---\left(1\right)$

In formula (1), ${\stackrel{\&OverBar;}{F}}_i^{\&prime;}={\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{F}_{i,j}^{\&prime;}/(k-1),$ ${\stackrel{\&OverBar;}{F}}^{\&prime;}={\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{F}_j^{\&prime;}/(k-1);$

STEP2.2. to correlation coefficient r _i(i ∈ [1..n]) carries out following zero correction, obtains one group of weight adjusting coefficient r ' _i, r ' _ishow more greatly forecast model f _ihigher with actual result correlativity;

$r_i^{\&prime;}=\left|r_i\right|-{\mathrm{\&Sigma;}}_{i=1}^n\left|r_i\right|/n;---\left(2\right)$

STEP3. computational prediction model f _i(i ∈ [1..n]) the m time result of calculation F ' _i,mwith actual result F ' _mdeviation Δ F _i:

STEP3.1. $\mathrm{\&Delta;}\stackrel{\&OverBar;}{F}=\frac{{\mathrm{\&Sigma;}}_{i=1}^n|F_{i,m}^{\&prime;}-F_m^{\&prime;}|}{n};---\left(3\right)$

STEP3.2. $\mathrm{\&Delta;}{F}_i=\mathrm{\&Delta;}\stackrel{\&OverBar;}{F}-|F_{i,m}^{\&prime;}-F_m^{\&prime;}|;---\left(4\right)$

Deviation Δ F _ilarger, show forecast model f _ithe m time forecasting accuracy high.

STEP4. computational prediction model f _ithe weight adjusting value Δ ω of (i ∈ [1..n]) _i,m:

STEP4.1. to correlation coefficient r ' _i(i ∈ [1..n]) and deviation Δ F _ispan normalization:

$r_i^{\&prime;}=\left|r_i\right|-{\mathrm{\&Sigma;}}_{i=1}^n\left|r_i\right|/n(r_i^{\&prime;}\&Element;[-\mathrm{1,1}\left]\right);---\left(5\right)$

$\mathrm{\&Delta;}{F}_i^{\&prime;}=\frac{\mathrm{\&Delta;}{F}_i+\min \left(\mathrm{\&Delta;}{F}_i\right)}{\max \left(\mathrm{\&Delta;}{F}_i\right)-\min \left(\mathrm{\&Delta;}{F}_i\right)}(\mathrm{\&Delta;}{F}_i^{\&prime;}\&Element;[-\mathrm{1,1}\left]\right);---\left(6\right)$

STEP4.2. computational prediction model f _ithe weight adjusting value Δ ω of (i ∈ [1..n]) _i,m

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_{i,m}={\mathrm{\&omega;}}_{i,m-1}\frac{(p_1{r}_i^{\&prime;}+p_2\mathrm{\&Delta;}{F}_i^{\&prime;})-{\mathrm{\&Sigma;}}_{i=1}^n(p_1{r}_i^{\&prime;}+p_2\mathrm{\&Delta;}{F}_i^{\&prime;})/n}{{\mathrm{\&Sigma;}}_{i=1}^n(p_1{r}_i^{\&prime;}+p_2\mathrm{\&Delta;}{F}_i^{\&prime;})}---\left(7\right)$

In formula (7), p ₁and p ₂be respectively correlation coefficient r ' _i, deviation Δ F _iweight, wherein p ₁+ p ₂=1 (p under default setting ₁=0.4p ₂=0.6).

STEP5. for each i ∈ [1..n], ω is calculated _i,m;

ω′ _i,m=ω _i,m-1+Δω _i,mi∈[1..n] (8)

${\mathrm{\&omega;}}_{i,m}=\frac{{\mathrm{\&omega;}}_{i,m}^{\&prime;}}{{\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,m}^{\&prime;}}---\left(9\right)$

Weight adjusting value Δ ω _i,mmeet return (ω _{1, m}, ω _{2, m}.., ω _i,m.., ω _n,m), algorithm exits.

Claims (1)

1. a self-adapting regulation method for linear combination prediction model weight, is characterized in that, in accordance with the following steps:

(1) initial weight is determined: set the numerical value of actual result first as F ' ₀, each forecast model f _ipredicted value be F ' _i, wherein i ∈ [1...n], calculates then the initial weight of each forecast model fi is meet the model that prediction effect is good first and there is higher initial weight, and ${\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,0}=1;$

(2) dynamic conditioning weight:

A, establish current totally to predict the outcome for m time and actual result, comprise the F ' that predicts the outcome of before except the m time k-1 time _{i, m-k+1}, F ' _{i, m-k+2}..., F ' _{i, m-1}, and the actual result F ' of first k time _m-k+1, F ' _m-k+2..., F ' _m; Wherein, k is time window, defaultly gets 5; As m < k, get k=m; Corresponding F ' _{i, m-k+1}, F ' _{i, m-k+2}..., F ' _{i, m-1}weight be respectively ω _{i, m-k+1}, ω _{i, m-k+2}..., ω _{i, m-1};

B, forecast model f _i, i ∈ [1...n], the result of calculation of k-1 time and the related coefficient of front k actual result before except the m time;

C, computational prediction model f _ithe deviation of the m time result of calculation and actual result,

D, result according to A, B, self-adaptation solves each forecast model f _ithe weights omega of the m time adjustment _{i, m}, wherein i ∈ [1...n], for the forecast model high and less with actual result deviation with actual result correlativity, increases the value of weight; For the forecast model low with actual result correlativity and the forecast model larger with actual result deviation, reduce the value of weight;

In described step (2), the specific algorithm of step B is:

STEP1. calculate $F_m={\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,m-1}{F}_{i,m}^{\&prime;};$

In order to avoid weight adjusting too frequently causes shake, as F ' _m=F _m=0 or | F ' _m-F _m|/(| F ' _m|+| F _m|)≤5%, do not carry out index weights adjustment, namely for each i ∈ [1...n], make ω _{i, m}=ω _{i, m-1}, return (ω _{1, m}, ω _{2, m}..., ω _{i, m}..., ω _{n, m}), algorithm exits;

STEP2. according to forecast model f _iresult of calculation and the related coefficient of actual result, determine weight adjusting coefficient:

STEP2.1. for each i ∈ [1...n], Pearson product-moment correlation coefficient PPMCC sequence of calculation F ' is adopted _{i, m-k+1}, F ' _{i, m-k+2}..., F ' _{i, m-1}with F ' _m-k+1, F ' _m-k+2..., F ' _m-1related coefficient, obtain one group of correlation coefficient r _i, r _i∈ [-1,1];

$r_i=\frac{{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}(F_{i,j}^{\&prime;}-{\stackrel{\&OverBar;}{F}}_i^{\&prime;})\left(F_j^{\&prime;}{-\stackrel{\&OverBar;}{F}}^{\&prime;}\right)}{\sqrt{{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{(F_{i,j}^{\&prime;}-{\stackrel{\&OverBar;}{F}}_i^{\&prime;})}^2{\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{\left(F_j^{\&prime;}{-\stackrel{\&OverBar;}{F}}^{\&prime;}\right)}^2}}---\left(1\right)$

In formula (1), ${\stackrel{\&OverBar;}{F}}_i^{\&prime;}={\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{F}_{i,j}^{\&prime;}/(k-1),$ ${\stackrel{\&OverBar;}{F}}^{\&prime;}={\mathrm{\&Sigma;}}_{j=m-k+1}^{m-1}{F}_j^{\&prime;}/(k-1);$

STEP2.2. to correlation coefficient r _icarry out following zero correction, obtain one group of weight adjusting coefficient r ' _i, i ∈ [1...n], r ' _ishow more greatly forecast model f _ihigher with actual result correlativity;

$r_i^{\&prime;}=\left|r_i\right|-{\mathrm{\&Sigma;}}_{i=1}^n\left|r_i\right|/n---\left(2\right)$

In described step (2), the specific algorithm of step C is:

Computational prediction model f _ithe m time result of calculation F ' _{i, m}with actual result F ' _mdeviation Δ F _i:

$\mathrm{\&Delta;}\stackrel{\&OverBar;}{F}=\frac{{\mathrm{\&Sigma;}}_{i=1}^n|F_{i,m}^{\&prime;}-F_m^{\&prime;}|}{n};---\left(3\right)$

$\mathrm{\&Delta;}{F}_i=\mathrm{\&Delta;}\stackrel{\&OverBar;}{F}-|F_{i,m}^{\&prime;}-F_m^{\&prime;}|---\left(4\right)$

Deviation Δ F _ilarger, show forecast model f _ithe m time forecasting accuracy high;

In described step (2), the specific algorithm of D step is:

STEP1. computational prediction model f _iweight adjusting value Δ ω _{i, m}:

STEP1.1. to correlation coefficient r _iwith deviation Δ F _ispan normalization:

$r_i^{\&prime;}=\left|r_i\right|-{\mathrm{\&Sigma;}}_{i=1}^n\left|r_i\right|/n,(r_i^{\&prime;}\&Element;[-\mathrm{1,1}\left]\right);---\left(5\right)$

${\mathrm{\&Delta;F}}_i^{\&prime;}=\frac{{\mathrm{\&Delta;F}}_i+\min \left({\mathrm{\&Delta;F}}_i\right)}{\max \left({\mathrm{\&Delta;F}}_i\right)-\min \left({\mathrm{\&Delta;F}}_i\right)},({\mathrm{\&Delta;F}}_i^{\&prime;}\&Element;[-\mathrm{1,1}\left]\right);---\left(6\right)$

Wherein: r ' _ifor r _inormalized value, Δ F ' _ifor Δ F _inormalized value;

STEP1.2. computational prediction model f _iweight adjusting value Δ ω _{i, m}

${\mathrm{\&Delta;\&omega;}}_{i,m}={\mathrm{\&omega;}}_{i,m-1}\frac{(p_1{r}_i^{\&prime;}+p_2{\mathrm{\&Delta;F}}_i^{\&prime;})-{\mathrm{\&Sigma;}}_{i=1}^n(p_1{r}_i^{\&prime;}+p_2{\mathrm{\&Delta;F}}_i^{\&prime;})/n}{{\mathrm{\&Sigma;}}_{i=1}^n(p_1{r}_i^{\&prime;}+p_2{\mathrm{\&Delta;}}_i^{\&prime;})}---\left(7\right)$

In formula (7), p ₁be correlation coefficient r ' _iweight, p ₂for deviation Δ F _iweight, wherein p ₁+ p ₂=1, p under default setting ₁=0.4, p ₂=0.6;

STEP2. for each i ∈ [1...n], ω is calculated _{i, m};

ω′ _i，m＝ω _i，m-1+Δω _i，mi∈[1...n] (8)

${\mathrm{\&omega;}}_{i,m}=\frac{{\mathrm{\&omega;}}_{i,m}^{\&prime;}}{{\mathrm{\&Sigma;}}_{i=1}^n{\mathrm{\&omega;}}_{i,m}^{\&prime;}}---\left(9\right)$

Weight adjusting value Δ ω _{i, m}meet return (ω _{1, m}, ω _{2, m}..., ω _{i, m}..., ω _{n, m}).