Development of forecasting model that can be used in a variety of subjects
Abstract
After more than 5 years of development, I have completed building up a unique election forecasting model early this year. Initially named Universal Trend Model, it has been tested as well as verified for 30 elections around the globe, though first of the two structure was applied for 703 cases in the past. Unlike many other election forecasts, this model does not include factors indirect from the polling data that some individuals consider to be affecting outcome of elections. As a result, even though it was developed mainly in purpose for accurately predicting election results, the model can be used in any other subjects by inputting base data of various topics.
After more than 5 years of development, I have completed building up a unique election forecasting model early this year. Initially named Universal Trend Model, it has been tested as well as verified for 30 elections around the globe, though first of the two structure was applied for 703 cases in the past. Unlike many other election forecasts, this model does not include factors indirect from the polling data that some individuals consider to be affecting outcome of elections. As a result, even though it was developed mainly in purpose for accurately predicting election results, the model can be used in any other subjects by inputting base data of various topics.
1. Background
1. Background
1.1 Basic Idea
1.1 Basic Idea
I want to first emphasize that this model was developed almost entirely based my own idea & insight, then gradually upgraded several times after analyzing the performances one-by-one. At first, my forecast model was thought to deal with election forecasting only. The most basic structure of the model is the combination of (size indicator x measurement indicator) & change over time. Size Indicator sets how much each data will influence the overall numbers. Measurement Indicator represents each unique data influencing the overall numbers. Change over time is calculated in the base of the product of two indicators above.
1.2 Related Concepts
1.2 Related Concepts
There are three key related mathematical concepts for better understanding of Multifield Forecasting Model: Normalization, Weighting Scheme, and Cumulative Error. Normalization is a term defined differently by in which area of subject it is mentioned, but I found several explanations that can be useful. According to Datacamp, “normalization refers to the process of adjusting values measured on different scales to a common scale.” From the view of database, normalization is the process of organizing data into specific structures to improve manageability, integrity, consistency. Weighting Schemes are system of applying weights to social indicators, and Cumulative Error is the integration of local errors in a series of measurements.
2. Methodology
2. Methodology
Structure 1
Structure 1
V1.1 | ... | V1.k |
... | | ... |
Vm.l | ... | Vm.k |
{n1*(rD1/tD1)}(=W1)/ΣW |
... |
{nk*(rDk/tDk)}(=Wk)/ΣW |
A1 |
... |
Am |
Structure 2
Structure 2
Σ[(ni/i)*{A1.i-A1.(i+1)}] |
... |
Σ[(ni/i)*{Am.i-Am.(1+1)}] |
T1.i |
... |
Tm.i |
n, A, T stands for Sample Size, Average, Trend. When it comes to election forecasting, i is the value representing days left until election day, ni equals to the sample size from structure 1 at the point i, A’cn’.i is the average support of the candidate/party with the number ‘cn’ assigned from structure 1 at the point i, and T’cn’.i refers to the trend of support of the candidate/party with the number ‘cn’ assigned at the point i.
Bridge Structure
Bridge Structure
F1 |
... |
Fm |
A1 |
... |
Am |
T1.i |
... |
Tm.i |
F stands for Forecasting.
Test
Test
Index | Date | Volume | RegionA(I1) | RegionB(I2,I3) |
Index1_1 | 1/3 | 350 | 158.94 | |
Index2_1 | 1/4 | 271 | | 99.38 |
Index3_1 | 1/4 | 258 | | 105.17 |
Index1_2 | 1/5 | 327 | 159.97 | |
Index1_3 | 1/6 | 370 | 158.73 | |
Index1_4 | 1/7 | 332 | 159.46 | |
Index2_2 | 1/7 | 272 | | 96.99 |
Index3_2 | 1/7 | 254 | | 105.21 |
Index1_5 | 1/10 | 335 | 160.02 | |
Index1_6 | 1/12 | 341 | 159.45 | |
Index2_3 | 1/12 | 264 | | 97.56 |
Index3_3 | 1/12 | 275 | | 105.18 |
Base Day = 1/13
In[]:=
nsum=n1/1+n2/2+n3/3+n4/4
Out[]=
5511
Data for 1/12 based on 1/5~1/12
In[]:=
n1=350*(0/1)+271*(0/1)+258*(0/1)+327*(1/1)+370*(1/1)+332*(1/1)+272*(1/1)+254*(1/1)+335*(1/1)+341*(1/1)+264*(1/1)+275*(1/1)
Out[]=
2770
In[]:=
M1={{158.94,0,0,159.97,158.73,159.46,0,0,160.02,159.45,0,0},{0,99.38,105.17,0,0,0,96.99,105.21,0,0,97.56,105.18}};
In[]:=
M2={{0/n1},{0/n1},{0/n1},{327/n1},{370/n1},{332/n1},{272/n1},{254/n1},{335/n1},{341/n1},{264/n1},{275/n1}};
In[]:=
N[MatrixForm[M1.M2]]
Out[]//MatrixForm=
98.1806 |
38.9115 |
A1 |
A2 |
98.1806 |
38.9115 |
In[]:=
TAB1=((n1/1)/nsum)*{{{98.1805631768953},{38.911537906137184}}-{{89.94944605208764},{44.30362133112856}}}
Out[]=
{{{4.13722},{-2.71023}}}
Data for 1/11 based on 1/4~1/11
In[]:=
n2=350*(0/1)+271*(1/1)+258*(1/1)+327*(1/1)+370*(1/1)+332*(1/1)+272*(1/1)+254*(1/1)+335*(1/1)+341*(0/1)+264*(0/1)+275*(0/1)
Out[]=
2419
In[]:=
M3={{0/n2},{271/n2},{258/n2},{327/n2},{370/n2},{332/n2},{272/n2},{254/n2},{335/n2},{0/n2},{0/n2},{0/n2}};
In[]:=
N[MatrixForm[M1.M3]]
Out[]//MatrixForm=
89.9494 |
44.3036 |
In[]:=
TAB2=((n2/2)/nsum)*{{{89.94944605208764},{44.30362133112856}}-{{98.66981220657277},{38.703669194655106}}}
Out[]=
{{{-1.91386},{1.22902}}}
Data for 1/10 based on 1/3~1/10
In[]:=
n3=350*(1/1)+271*(1/1)+258*(1/1)+327*(1/1)+370*(1/1)+332*(1/1)+272*(1/1)+254*(1/1)+335*(1/1)+341*(0/1)+264*(0/1)+275*(0/1)
Out[]=
2769
In[]:=
M4={{350/n3},{271/n3},{258/n3},{327/n3},{370/n3},{332/n3},{272/n3},{254/n3},{335/n3},{0/n3},{0/n3},{0/n3}};
In[]:=
N[MatrixForm[M1.M4]]
Out[]//MatrixForm=
98.6698 |
38.7037 |
In[]:=
TAB3=((n3/3)/nsum)*{{{98.66981220657277},{38.703669194655106}}-{{112.25008627773212},{44.03059161873459}}}
Out[]=
{{{-2.27447},{-0.89217}}}
Data for 1/9 based on 1/2~1/9
In[]:=
n4=350*(1/1)+271*(1/1)+258*(1/1)+327*(1/1)+370*(1/1)+332*(1/1)+272*(1/1)+254*(1/1)+335*(0/1)+341*(0/1)+264*(0/1)+275*(0/1)
Out[]=
2434
In[]:=
M5={{350/n4},{271/n4},{258/n4},{327/n4},{370/n4},{332/n4},{272/n4},{254/n4},{335/n4},{0/n4},{0/n4},{0/n4}};
In[]:=
N[MatrixForm[M1.M5]]
Out[]//MatrixForm=
112.25 |
44.0306 |
In[]:=
TABi=TAB1+TAB2+TAB3
Out[]=
{{{-0.0511126},{-2.37338}}}
TA.i |
TB.i |
-0.0511126 |
-2.37338 |
In[]:=
FAB={{{98.1805631768953},{38.911537906137184}}+{{-0.05111257409047587},{-2.373376587840108}}}
Out[]=
{{{98.1295},{6.13183×}}}98.1295
9
10
FA |
FB |
98.1295 |
36.5382 |
New Index of Region A will be at 98.1295 as of Base Day, New Index of Region B will be at 36.5382 as of Base Day
3. Overview
3. Overview
The effect of Multifield Forecasting Model is the satisfaction on right to know, accurate public opinion, improved data, and setting of related policy or diplomacy in advance. There aren’t many forecasting models that works over the lines of fields, so I would say application of my model into lots of topic will be influential. This model could not have a correct outcome if proper measurements for each topic aren’t selected. Details of the model are included on the paper that is being prepared.
4. Bibliography
4. Bibliography
GeeksforGeeks. “Introduction to Database Normalization.” GeeksforGeeks, October 9, 2025. https://www.geeksforgeeks.org/dbms/introduction-of-database-normalization/.
Gomstyn, Alice, and Alexandra Jonker. “What Is Database Normalization?” IBM. Accessed November 26, 2025. https://www.ibm.com/think/topics/database-normalization.
Lakshmikantham, V., and S.K. Sen. “Error and Complexity in Numerical Methods.” In Mathematics in Science and Engineering/Mathematics in Science and Engineering, 147–93, 2005. https://doi.org/10.1016/s0076-5392(05)80056-6. 5
Land, K.C. (2023). Weighting Schemes. In: Maggino, F. (eds) Encyclopedia of Quality of Life and Well-Being Research. Springer, Cham. https://doi.org/10.1007/978-3-031-17299-1_3208.
Shaibu, Samuel. “Normalization Vs. Standardization: How to Know the Difference,” October 15, 2024. https://www.datacamp.com/tutorial/normalization-vs-standardization.