CC BY
27UDC 338.2(476)+316.42(476) https://doi.org/10.33619/2414-2948/40/31
JEL classification: H10, J58, P35, Z13
INTRODUCTION OF THE METHOD OF HARMONIC WEIGHTS AND INTEGRATED ECONOMIC AND STATISTICAL CALCULATIONS IN THE ANALYSIS OF SOCIO-ECONOMIC SECURITY
©Shvaiba D., ORCID: 0000-0001-6783-9765, Ph.D., Belarusian Trade Union of workers of chemical, mining and oil industries, Belarusian national technical University, Minsk, Belarus, shvabia@tut.by
ВНЕДРЕНИЕ МЕТОДА ГАРМОНИЧЕСКИХ ВЕСОВ И УКРУПНЕННЫХ ЭКОНОМИКО-СТАТИСТИЧЕСКИХ РАСЧЕТОВ ПРИ АНАЛИЗЕ ПОКАЗАТЕЛЕЙ СОЦИАЛЬНО-ЭКОНОМИЧЕСКОЙ БЕЗОПАСНОСТИ
©Швайба Д. Н., ORCID: 0000-0001-6783-9765, канд. экон. наук, Белорусский профсоюз работников химической, горной и нефтяной отраслей промышленности, Белорусский национальный технический университет, г. Минск, Беларусь, shvabia@tut.by
Abstract. In the implementation of comparative analysis of the application of methods of harmonic weights and integrated economic and statistical calculations in the analysis of socioeconomic security characteristics, the priority is given to the method of integrated economic and statistical calculations. When predicting the characteristics of socio-economic security by the method of integrated economic and statistical calculations, their absolute levels or the dynamics of their growth are used. The use of the absolute values of socio-economic security characteristics in forecasting seems more appropriate, as it is possible to solve a number of problems of the method — to identify the levels of factors and factors K_ xi in the lead period.
Аннотация. При реализации сравнительного анализа применения методов гармонических весов и укрупненных экономико-статистических расчетов при анализе характеристик социально-экономической безопасности приоритет отдан методу укрупненных экономико-статистических расчетов. При прогнозировании характеристик социально-экономической безопасности методом укрупненных экономико-статистических расчетов применяются их абсолютные уровни либо динамика их роста. Использование при прогнозировании абсолютных значений характеристик социально-экономической безопасности видится более целесообразным, т. к. представляет возможность решить ряд проблем метода — выявить уровни факторов и коэффициентов K_xi в периоде упреждения.
Keywords: socio-economic security, government, society, enterprise, employee, threat, security, interests, economics, analysis, system.
Ключевые слова: социально-экономическая защищенность, государство, общество, предприятие, работник, угроза, защищенность, интересы, экономика, анализ, система.
When creating a predictive model using the harmonic weights method, the subsequent time series levels are assigned greater weights compared to the previous ones [1-3].
Бюллетень науки и практики /Bulletin of Science and Practice http ://www.bulletennauki.com
Т. 5. №3. 2019
Time series of levels of socio-economic security characteristics Yt (t=1, 2, ..., n) divided into 2-ve components
Yt = <K0 + et
(1)
where: ^(t)— a function of the time trend. st — random component.
With the help of the constructed model, forecast values are calculated Yt and forecast error in the period a(li)Sw in (t+1) period (l=1,2, ..., L).
Let us consider the method of formation of the forecast model by the method of harmonic weights based on the forecast of the number of threats (Table 1.).
Table 1.
DYNAMICS OF THE NUMBER OF THREATS IN T-8-T YEARS
Years t-8 t-7 t-6 t-5 t-4 t-3 t-2 t-1 t
Threats 218 233 255 287 335 403 498 610 762
t 1 2 3 4 5 6 7 8 9
Source: elaboration of author.
Using the least squares method, we calculate the exponents of the equations of linear segments, taking the length of the period (k) equal to 5 (Tables 2-3).
INTERMEDIATE CALCULATIONS FOR CALCULATING THE TREND PARAMETERS OF THE 1st SEGMENT
Table 2.
№ Year Y t Yt t2
1 t-8 218 1 218 1
2 t-7 233 2 466 4
3 t-6 255 3 765 9
4 t-5 287 4 1148 16
5 t-4 335 5 1675 25
I — 1328 15 4272 55
Source: elaboration of author.
The system of normal equations will have the form:
1328 = 5a0 + 15a1 4272 = 15a0 + 55a1
3984 = —15a0 - 45a1 4272 = 15a0 + 55a1 288 = 10a1; a1 = 28.8
1328 — 15 x 28.8 a0 =---= 179.2
3
Table 3.
INTERMEDIATE CALCULATIONS FOR CALCULATING THE TREND PARAMETERS OF THE 2nd SEGMENT
№ Year Y t У t2
1 t-7 233 2 466 4
2 t-6 255 3 765 9
3 t-5 287 4 1148 16
4 t-4 335 5 1675 25
5 t-3 403 6 2418 36
I — 1513 20 6472 90
Source: elaboration of author.
a0 = 134.6; a1 = 42.
Trend parameters for all phases of the moving trend are also calculated. The number of equations is revealed by the formula:
n-k+1=9-5+1=5 F1(t) = 179.2 + 28.8t (t = 1, 2, 3,4, 5)
r2(t) = 134.6+ 42.0t (t = 2,3,4,5,6)
y3(t) = 54.6 + 60.2t (t = 3,4, 5,6, 7)
J4(t) = -58.8 + 80.9t (t = 4, 5,6, 7, 8)
r5(t) = -221.1 + 106.1t (t = 5, 6, 7,8,9)
Using these equations, the values of the moving trend are calculated Yj(t): in points t=1 and t=9 mychelleusa 1 — the value f1(t) and F9(t);
in points t=2 and t=8 — value F2(t) and F8(t) mychelleusa 2 — um values V2(t) andy8(t) etc.
r2(t) =
r1(t) = 179.2 + 28.8 X 1 = 208 (179.2 + 28.8t) + (134.4 + 42.0t) (179.2 + 28.8 X 2) + (134.6 + 42.0 X 2)
= 227.7
2 2 In the following, we also substitute the corresponding value t into the corresponding number of models:
Y3(t) = (179.2+28.8x3) + (134.6+42.0x3) + (54.6+60.2x3)^253 Q
^_(179.2 + 28.8x4)+(134.6+42.0x4)+(54.6+60.2x4) (-58.8+80.9x4)_
4(t)--4-+-4--289.3
(179.2 + 28.8 x 5) + (134.6 + 42.0 x 5) + (54.6 + 60.2 x 5)
*5(t) = ■
5
*6(t) -
(-58.8 + 80.9 X 5) + (-221.1 + 106.1 X 5 + ---- 335.7
(134.6 + 42.0 X 4) + (54.6 + 60.2 X 4) (-58.8 + 80.9 X 6) + (-221.1 + 106.1 X 6)
4 + 4
- 411.125
(54.6 + 60.2 X 7) (-58.8 + 80.9 X 7) + (-221.1 + 106.1 X 7)
%) -
>8(t) -
3 + 3
(-58.8 + 80.9 X 8) + (-221.1 + 106.1 X 8)
- 501.7
2
y9(t) - -221.1 + 106.1 X 9 - 733.8
- 608.05
Based on these values iy(t) calculate the gains by the formula:
^t+i = *t+i - ^t = 227.7 - 208.0 = 19.7 = 253.8- 227.7 = 26.1 = 289.3 - 253.8 = 35.5 = 335.7 - 289.3 = 46.4 = 411.125 - 335.7 = 75.425 = 501.7 - 411.125 = 90.575 = 608.05 - 501.7 = 106.35 = 733.8 - 608.05 = 125.75
The average growth is calculated by the formula
n—1
0)
—I
C^i ш
(2)
t+i
t=i
where — the coefficients, giving follow-up information compared with the previous large weights.
Они должны удовлетворять следующим условиям:
Ctn+i>0 (t=1, 2, ..., n-1)
n-1
''t+1
IL— 1
I
t=1
rn =1
WA1 — 1
(3)
(4)
Coefficients Ctr+1 calculated by dividing the harmonic weights by n-1. Harmonic weights my calculated by the formula:
1
mt+1 — mt + (t — 2, 3,..., n — 1)
(5)
In this case, for a point t=2
Ш2
n-1 9—1
— 0.125
m3 — ш2 + ■
n
m4 — ш3 + ■
n
ш5 — ш4 +
n
ш6 — ш5 + ■
n
ш7 — ш6 + ■
n
ш8 — ш7 + ■
n
ш9 — ш8 +
— 0.125 +
— 0.268 +
— 0.435 +
9
9
9
— 0.635 +
9
— 0.885 +
— 1.218 +
9
9
-- — 1.718+ -
п- 8 9
In practice, statistical tables of harmonic weights are o
0.268 0.435 0.635 0.885 1.218 1.718 2.718
ten used [4] (Table 5).
1
1
After calculating the value of the harmonic weights, we calculate Ct+1
0.125 C2 =-= 0.0156
2 8
0.268
C3 =-= 0.0335
38
0.435 C4 = —— = 0.0544 8
0.635 C5 = —— = 0.0794 58
0.885
C6 = —q— = 0.1106
1.2818
C7 =-= 0.1522
78
1.718 C8 = —-— = 0.2147
2.7818
C9 = —-— = 0.3397
In that case:
û = Ш=-1 Ctn+1 œt+i = 94.4752 (6)
19.7x0.0156=0.3073 23.1x0.0335=0.8744 35.5x0.0544=1.9312 46.4x0.0794=3.6842 75.425x0.1106=8.3420 90.575x0.1522=13.7855 106.35x0.2147=22.8333 125.75x0.3397=42.7173
94.4752
Value Sw can be defined by the formula:
Sw = Vit-1 Ctn+1 (wt+1 - Ö3)2 = V1021.55 = 31.9617 (7)
0.0156 X (19.7 - 94.4752)2 = 87.2247 0.0335 X (26.1 - 94.4752)2 = 156.6181 0.0544 X (35.5 - 94.4752)2 = 189.2072 0.0794 X (46.4 - 94.4752)2 = 183.5112 0.1106 X (75.425 - 94.4752)2 = 40.1378 0.1522 X (90.575 - 94.4752)2 = 2.3152 0.2147 X (106.35 - 94.4752)2 = 30.2750 0.3397 X (125.75 - 94.4752)2 = 332.2650 1021.554
The value of a (l) is calculated by the formula:
n-i (8) a(l) = a ) Ctn+1 (l = 0,1,2,..., n - 1)
t=i
a for this example, take 4.
a(l1) = (0.3397 + 0.2147) X 4 = 2.2176 a(l2) = (0.3397 + 0.2147 + 0.1522) X 4 = 2.8264 a(l3) = (0.3397 + 0.2147 + 0.1522 + 0.1106) X 4 = 3.2688 a(l4) = (0.3397 + 0.2147 + 0.1522 + 0.1106 + 0.0794) X 4 = 3.5864 a(l4) = (0.3397 + 0.2147 + 0.1522 + 0.1106 + 0.0794 + 0.0544) X 4 = 3.8040 To calculate the highest and lowest variants of the equations of socio-economic security are calculated a(l1)Sw
a(l1)Sw = 2.2176 X 31.9617 = 70.8783 a(l2)Sw = 2.8264 X 31.9617 = 90.3365 a(l3)Sw = 3.2688 X 31.9617 = 104.4764 a(l4)Sw = 3.5864 X 31.9617 = 114.6274 a(l5)Sw = 3.8040 X 31.9617 = 121.5823
Forecast levels of socio-economic security are calculated by the formula:
Fit+1 = + S = 733.8 + 94.4752 = 828.2752 ^t+2 = + S = 828.2752 + 94.4752 = 922.7504 F*t+3 = F*t+2 + S = 922.7504 + 94.4752 = 1017.225 rt+5 = + S = 1111.700 + 94.4752 = 1206.176 F*t+4 = F*t+3 + S = 1017.225 + 94.4752 = 1111.700
The largest and smallest options for ensuring socio-economic security [5] are calculated by the formulas:
^*n+1 + ^ (0SW
757.3969 832.4139 = 912.749 = 997.073 = 1084.593 = 899.153 1013.086 1121.701 = 1226.327 = 1327.758
F*t+1 - a(Z1)5w = 828.2752 - 70.8783 = F%+2 - = 922.7504 - 90.3365 =
F*t+3 - a(Z3)5w = 1017.225 - 104.4764 F%+4 - a(*4)Sw = 1111.700 - 114.6274 F%+5 - a(Z5)Sw = 1206.176 - 121.5823 F*t+1 + a(Z1)5w = 828.2752 + 70.8783 F%+2 + a(Z2)5w = 922.7504 + 90.3365 : F*t+3 + a(Z3)5w = 1017 + 104.4764 = F%+4 + a(Z4)Sw = 1111.700 + 114.6274 F%+5 - a(Z5)5w = 1206.176 + 121.5823 The obtained forecast indicators are formed in the Table 4.
FORECASTED VALUE У*ж, У*ж ± a(/)SM
Table 4.
Years t v* 1 t+1 ш l a(Z) a(Z)Sw v* r t+г + a(i)Sw v* r t+г - a(i)5w
t+1 10 828.2752 94.4752 1 2.2176 70.8783 899.153 757.3969
t+2 11 922.750 94.4752 2 2.8264 90.3365 1013.086 832.4139
t+3 12 1017.225 94.4752 3 3.2688 104.4764 1121.701 912.749
t+4 13 1111.700 94.4752 4 3.5864 114.6274 1226.327 997.073
t+5 14 1206.176 94.4752 5 3.8040 121.5823 1327.758 1084.593
Source: elaboration of author.
Бюллетень науки и практики / Bulletin of Science and Practice http ://www.bulletennauki.com
Т. 5. №3. 2019
Based on Table 4 we build a graph of the dynamics of actual and forecast data of indicators of socio-economic security in t + 1 — t + 5 years (Figure). 1600
1400 1200 1000 800 600 400 200
0
t-8 t-7 t-6 t-5 t-4 t-3 t-2 t-1 t t+1 t+2 t+3 t+4 t+5 годы
Figure. Dynamics of actual and forecast levels of socio-economic security in the t + 8 — t + 5 years. Source: elaboration of author.
-actual levels of socio-economic security in the t + 8 — t years; -forecast levels of socio-economic security in the t + 8 — t + 5 years. At the same time, the method of integrated economic and statistical calculations is based on the study of numerical relations between the data of socio-economic security and their extrapolation in the forecast period [6-8]. Predictive models will look like:
(9)
where: Y — forecast levels of an effective indicator of socio-economic security;
j — options (minimum, medium and maximum);
Xj — factors (economic, social, etc., indicators) (i=1, ..., n));
T — the forecast to year forecast period;
L — years of lead time (l=1, ..., L).
When forecasting socio-economic security data by the method of integrated economic and statistical calculations, their absolute levels or the dynamics of their growth are used. The use of absolute data in forecasting indicators of socioeconomic security seems more appropriate because it is possible to solve a number of problems of the method to identify the levels of factors and coefficients in the lead period.
The calculation of the coefficient levels can be a certain difficulty in the lead period.
Based on the theory in the time series of coefficients characterizing the ratio of the resulting indicator of socio-economic security to the factors of each year of the retrospective period, the level of coefficients can be constant (approximately constant) or in their series there will be a tendency to increase (decrease) [8].
о <N 3.598
OS 3.54 2.598
00 3.495 2.548 2.098
f- 3.440 2.495 2.048 1.764
o 3.381 2.440 1.955 1.714 1.514
tn 3.318 2.381 1.940 1.662 1.464 1.314
^ 3.252 2.318 1.881 1.606 1.412 1.264 1.148
d 3.180 2.252 1.818 1.547 1.356 1.212 1.098 1.005
<N 3.103 2.180 1.752 1.485 1.297 1.156 1.045 0.955 0.880
- 3.020 2.103 1.680 1.418 1.235 1.097 066 0 0.902 0.830 0.769
О 9 2 OS 0 2 о 3 0 ю ro 8 5 3 © 3 OS 7 4 00 7 7 r- 9 r- 9 6
.2 .2 ^ ^ .0 .0 .0 .0 .0
OS 9 2 00 9 2 OS 0 2 0 <N 9 © 8 6 OS 8 6 00 8 8 r- 2 2 f- 6 6 ю 9 \o 8 7
.2 ^ .0 .0 .0 .0 .0 .0 .0
00 00 9 2 00 9 2 00 0 2 о 9 00 2 0 00 5 2 f- 3 6 ю \o 6 6 8 2 ич 5 9
.2 ^ ^ ^ .0 .0 .0 .0 .0 .0 .0 .0
f- 3 9 00 9 2 ro \D 9 О f- 3 OS 0 2 00 0 3 f- 9 5 0 0 2 5 ич 5 7 4 4 8
.2 ^ ^ .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
o 0 5 3 9 00 <N \D 9 OS \D 00 3 3 5 ю 8 4 3 9 8 2 5 0 2 2 9 ro 7 6 ro 5 4 ro
.2 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
tn 3 00 <N 0 5 3 9 о 5 00 00 \D l> \D 0 0 2 6 3 2 9 8 ro 16 ro 6 3 ro 5 ro 6 9 <N 0 8 <N
.2 ^ ^ .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
^ 3 00 о 3 00 <N 0 5 OS 0 5 3 \D 9 2 5 00 ro 5 ro 3 2 ro 8 9 <N 8 7 <N 9 5 <N 4 2 <N 0 3 <N 7 <N
.2 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
d 3 3 00 3 00 о 3 00 o 5 3 9 f-ГО \D 3 ro 2 0 ro <N 15 <N 2 3 <N 5 <N 10 <N 8 00 7 f- 7 8
^ ^ .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
<N 0 0 3 3 00 3 00 0 5 t> ro 0 ro 00 <N \D 3 <N <N OS f- 0 8 8 d 9 <N <N 4 8 о 3 о
.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
0 0 3 3 ro 0 5 <N 0 0 <N 3 5 <N 0 О 19 о 3 00 о o 17 © 7 6 © 3 6 О 9 5 © 6 5 © 3 5 о 0 5
.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0
- <N d \D f- 00 OS О - <N d U4 \D 00 OS о <N
5 le
lab
н
In the 1st case (the level of coefficients in the pre-forecast period is stable) when searching for the level of coefficients in the period of anticipation of difficulties does not occur (their level in the forecast period will be taken equal to the level in the retrospective period). In a situation where there is a clear tendency to increase and there are no cycles in the time series of these coefficients when their level is found during the lead time, it makes sense to apply the following approach:
a) set the value and value of the difference between each subsequent and previous coefficient (the value of "plus" is inherent in time series of coefficients with a tendency to increase,
"minus" — with a tendency to decrease);
b) by dividing the sum of the increments of the coefficients by the number of these increments, calculate the average annual change in the level of the coefficients AK^ in the retrospective period;
c) by summation with the level of the coefficient in the last year of the retrospective period of its average annual change, we obtain the level of this coefficient in the 1st year of the lead period.
d) as a result of such iterations (point "b") we find the level of coefficients characterizing the ratio of the level of socio-economic security to the levels of factors in each year of the lead period, in other cases (the presence of cycles, it is difficult to identify any pattern in the change in the coefficients, etc.) it is necessary to apply individual or group expert assessments.
When calculating the minimum and maximum level of coefficients we will proceed from the proposal that the ratio of the levels of the resulting indicator of socio-economic security and the factors in the lead-up period can not be lower than achieved, i.e. the level of the coefficient in each year of the lead-time period, the ratio may not be lower than in the last year (s) of the retrospective period. Naturally, this premise is conditional, since the presence of time series of coefficients should be allowed from the theory with dynamics to reduction. But in the long-term forecasting factors, in the time series of which the coefficients they tend to decrease, it is impractical to apply, due to the fact that there may come a moment t, in which a logical interpretation of the revealed result will be impossible. In this regard, it seems reasonable to use in determining max min the following approach:
-consider the level min in the final year of the pre-emption period corresponding to the level of this coefficient in the final year of the retrospective period;
-consider the level max equal to the sum of the level and maximum value in the pre-forecast period.
To study trends in time series of socio-economic security characteristics, factors and coefficients it is necessary to apply the primary information for a longer period.
0.070 + 0.080 + 0.071 + 0.078 AKxi =---= 0.075
Atfx2 = 0.038 Atfx3 = 0.002
The predictive model of coefficients ^¿(t + Z) will have the form ^¿(t + Z) = ^¿(t) + A^Xjt, where t+1 — year of lead periothe d (l=1, ..., L).
Then:
+ Omin = 1.450; + Ocp = 1.450 + 0.075t;
^xi(t + i)max = 1.450 + 0.082t;
+ Omin = 2.183; + Ocp = 2.183 + 0.038t;
^x2(t + i)max = 2.183 + 0.051t;
+ Omin = 1.865; + Ocp = 1.865 + 0.002t;
^x2(t + i)max = 1.865 + 0.0031t;
Predictive models to identify the minimum, average and maximum options for the characteristics of socio-economic security, formed by the method of integrated economic and statistical calculations, will have the form:
rmin = 71.450x x 2.183x2 x 1.865x3
rcp = V(1.450x + 0.075t) x x1(2.183 + 0.038t) x x2(1.865 + 0.02t) x x3
rmax = V(1.450x + 0.0805t) x x1(2.183 + 0.051t) x x2(1.865 + 0.003t) x x3 where: t for the 1-year period of pre-emption equal to 1 (Table 6).
Table 6.
PRIMARY INFORMATION TO IDENTIFY PREDICTIVE OPTIONS FOR INCREASING SOCIO-ECONOMIC SECURITY BY THE METHOD OF INTEGRATED ECONOMIC AND STATISTICAL CALCULATIONS
Year A^s
t-4 1.151 2.029 1.857
t-3 1.221 0.070 2.069 0.040 1.858 0.001
t-2 1.301 0.080 2.120 0.051 1.861 0.003
t-1 1.372 0.071 2.152 0.032 1.864 0.003
t 1.450 0.078 2.183 0.031 1.865 0.001
Source: elaboration of author.
Limits of mathematical nature to the selection of factors included in the model, the method of integrated economic and statistical calculations does not show, in connection with which different options for the selection of factors are possible [10-11].
When implementing a comparative analysis of the application of methods of harmonic weights and integrated economic and statistical calculations in the analysis of socio-economic security characteristics, the priority is given to the method of integrated economic and statistical calculations. When forecasting the characteristics of social and economic security by the method of integrated economic and statistical calculations, their absolute levels or the dynamics of their growth are used. Use in predicting the absolute values of the characteristics of the socio-economic security sees more appropriate because it is possible to solve a number of problems of the method to identify the levels of factors and coefficients Kxi in the lead period.
References:
1. Kildishev, G. S., & Frenkel, A. A. (1973). Analiz vremennykh ryadov i prognozirovanie. Moscow, Statistika, 103. (in Russian).
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9. Shvaiba, D. (2019). Dynamic regression models of forecasting indicators of social and economic security Bulletin of Science and Practice, 5(1), 249-257.
10. Shvaiba, D. (2018). Socio-economic security of the hierarchical system. Bulletin of Science and Practice, 4(6), 248-254.
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Работа поступила Принята к публикации
в редакцию 17.02.2019 г. 21.02.2019 г.
Cite as (APA):
Shvaiba, D. (2019). Introduction of the method of harmonic weights and integrated economic and statistical calculations in the analysis of socio-economic security. Bulletin of Science and Practice, 5(3), 250-261. https://doi.org/10.33619/2414-2948/40/31.
Ссылка для цитирования:
Shvaiba D. Introduction of the method of harmonic weights and integrated economic and statistical calculations in the analysis of socio-economic security // Бюллетень науки и практики. 2019. Т. 5. №3. С. 250-261. https://doi.org/10.33619/2414-2948/40/31.
