Trend models for the analysis of socio-economic security Текст научной статьи по специальности «Строительство и архитектура»

UDC 338.2(476)+316.42(476) http://doi.org/10.5281/zenodo.2539765

JEL Classification: H10, J58, P35, Z13

TREND MODELS FOR 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

ТРЕНДОВЫЕ МОДЕЛИ ДЛЯ АНАЛИЗА 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. The correctness of the trend choice for forecasting the characteristics of socioeconomic security statistics can be qualified by the mean square error and the aspect of "Ascending" and "Descending" series (although there are other aspects, for example, the aspect based on the median of the sample). According to the proposed model, it is possible to predetermine the average monitoring errors for the development of the lower and upper limits of the forecast version of the values of the characteristics of socio-economic security statistics. The creation of a model is a rather labor-intensive process, as a result of which it is advisable to use, as a rule, the deterministic component of trend models when predicting the characteristics of socio-economic security statistics.

Аннотация. Корректность выбора тренда для прогнозирования характеристик статистики социально-экономической безопасности возможно квалифицировать при помощи величины среднеквадратической ошибки и аспекта «Восходящих» и «Нисходящих» серий (хотя есть и иные аспекты, к примеру, аспект, базирующийся на медиане выборки). По предложенной модели возможно предопределять средние ошибки мониторинга для разработки нижнего и верхнего пределов прогнозного варианта значений характеристик статистики социально-экономической безопасности. Создание модели — довольно трудозатратный процесс, вследствие чего при прогнозировании характеристик статистики социально-экономической безопасности целесообразно применять, как правило, детерминированную составляющую трендовых моделей.

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.

The correctness of the trend selection for predicting the characteristics of socio-economic security statistics can be qualified by means of the mean square error and the aspect of the "Ascending" and "Descending" series (although there are other aspects, for example, the aspect based on the median of the sample) [1].

The aspect of the "Ascending" and "Descending" series is based on the analysis of deviations of the calculated levels of socio-economic security statistics from those available in the time series. Range 8X, s2,..., sn, demonstrating the difference between the available (Yj) and settlement (Yj) indicators of a time series of levels of characteristics of socio-economic security statistics, changing the sequence of pros and cons, calculated by comparing the varieties of a number of random variables (8j+1 — 8j) with 0. If 8j+1 — 8j > 0, the plus sign is affixed if 8j+1 — 8j < 0, that is put down a minus sign. If there are 2 adjacent values 8j+1 = 8j and 8j+1 = 0, the is growing only one of them. The total sum of pluses and minuses will be less than or equal to n, where n is the number of random variables. The series length is calculated from a number of pros and cons KMax, which is characterized by the number of consecutive pluses and minuses and the number of series V(n).

The assumption about the random nature of deviations of empirical values of the time series from the trend for the 5% significance value is not rejected, if the next 2 circumstances are made:

1

K(n) > -

(2n - 1) - 1,96

16n — 29

90

(1)

^max(n) ^ Ко<Х)

(2)

Value K0(n) it is calculated as follows: n < 26 equal to 5, when 26 < n < 153 and 153 < n < 1170 K0 equals 6 and 7.

The deviation grounds have all chances to be an incorrect trend configuration, a very impressive length of the longest series, a short dynamic series, a small number of series, etc. The standard error is found by the formula:

a =

|ZP=i(Yj—Y]) N — p — 1

(3)

where: Yj — available levels of socio-economic security statistics; Yj— calculated levels of socio-economic security statistics; N — number of data levels of socio-economic security statistics in the time series; p — the number of parameters of the trend model.

We will determine the characteristics of the trend model, calculate the standard error and use the aspect of "Ascending" and "Descending" series on the model of linear form (for the remaining models we will give the final results without preliminary calculations) (Table 1, 2). The system of normal equations will be as follows

ZF = a0N + a1Zt ZFt = a0Zt + a12t2

(4)

f 87067 = 16a0+ 136a1 (867980 = 136a0 + 1496%

ao

ZF ZF zn Zt2

87067 136 867980 1496

N zt 16 136

Zt zt2 136 1496

= 224,925

Бюллетень науки и практики /Bulletin of Science and Practice http ://www.bulletennauki.com

Т. 5. №1. 2019

N ZY Zt ZYt

16 87067 136 867980

N Zt Zt Zt2

16 136 136 1496

= 376,207

The trend model of the linear form takes the form Y = 2243,925 + 376,207t, where t for t + 1 r. = 17.

Using this model, we calculate the values of Y in t — 15 — t and define the valueYj — Yj (table 5.6. column (6). If Yj — Yj > 0, the sign "+", when Yj — Yj < 0 — "-".

Table 1.

PRIMARY DATA AND PRELIMINARY CALCULATIONS FOR CALCULATING THE PARAMETERS OF THE TREND MODEL OF THE LINEAR FORM

Год Y t n t2

1 2 3 4 5 6

t-15 3450 1 3450 1 -829.868

t-14 2570 2 7140 4 -573.661

t-13 3720 3 11160 9 -347.453

t-12 3890 4 15560 16 -141.246

t-11 4015 5 20075 25 +109.961

t-10 4135 6 24810 36 +366.169

t-9 4430 7 31010 49 +447.376

t-8 4639 8 37112 64 +614.583

t-7 5074 9 45666 81 +555.791

t-6 5317 10 53170 100 +688.998

t-5 5660 11 62260 121 +722.205

t-4 6270 12 75240 144 +488.413

t-3 6968 13 90584 169 +166.620

t-2 7748 14 108472 196 -237.173

t-1 8625 15 129375 225 -737.965

t 9556 16 152896 256 -1292.758

E 87067 136 867980 1496 -4160ю124

+4160ю166

Source: elaboration of author.

The standard error will be equal to ±639,534:

l(-829,868)2 + - + (1292,758)2 *= l(-;6-1-1-^=±639,534

From Table 2. you can see that = 7, V(n)=4. Thus, the trend model of the linear form does not make sense to use for forecasting the data of economic statistics, because

1

Пп) > -

29

(2 x 16 - 1) - 1,96 (16 x 16 - — ^c(n) = 5

= 7,220

Trend models 2-16 will look like:

Yt = 3806,217 - 144,5828t + 30,63514t2,

44256 67

Yt = 6376,873 - 44256,67 c t

199933 7 1564967

rt = 8116,604 - 199933,7 + 19 c t t2

Yt = (0,0002990973 - 0,000000907865t)-1,

Yt = (0,0002990973 - 0,000000907865t - 0,000000002060924t2)-1,

Yt = 1160,220 X t0'3540418,

Yt = 2644,263 + 4412,476 Igt,

Yt = 17837,59 - 21601,6111Z#t + 7839,529 Z#t2,

Yt = 0,7016990 X t^743727 + 34 12,9 54,

Yt = 2930,298 X 1,006697t,

Yt = 2930,298 X e°.°06675617t,

Yt = 522,414 X e°,°1582776t + 2849,258,

П =-"-,

c 0,006711343+0,000922244311

Y =_i_

1 0,0005123886+0,0003330353 t—0,000001416418t2'

Yt = V2055910 - 413294,4t = 5085,797t2,

Table 2.

THE TOTAL NUMBER OF SERIES AND THE LENGTH OF THE LONGEST OF THE SERIES K

CALCULATED FOR MODELS 1-16

(N),

Vi = 4 tf 1 = 7 V9 = 3 К9 = 8

Ъ = 7 tf = 5 ^10 = 7 = 5

V3 = 2 tf = 10 Vn = 5 Кц = 7

V4 = 3 = 8 V12 = 4 ^12 = 7

V5 = 7 ^5 = 5 ^13 = 8 ^13 = 4

^ = 8 ^6 = 3 ^14 = 4 = 7

У7 = 4 К7 = 8 V15 = 8 ^15 = 3

^8 = 2 ^8 = 8 V16 = 5 ^16 = 6

Source: elaboration of author.

As a result of the application of the aspect of "Ascending" and "Descending" series, it is revealed that trend models 6, 13, 15 adequately characterize the dynamics of data levels of socioeconomic security statistics in t-15^t.

According to the models, the presence of cycles in a time series of levels of socio-economic security statistics was studied (Table 3.).

Elaboration of Table 3. allows to recognize that in a time series of values of characteristics of social and economic security statistics it is impossible to note exact cycles, but in the column 2nd and 3rd there are on 2 four-year cycles, in the 2nd, third and fourth-according to it 1, 2, 3 and 2 three-year. However, this does not represent a basis for the conclusion about the presence of cycles in a time series of values of characteristics of socio-economic security statistics because these cycles do not coincide in time, there is no clear priority of exceeding the actual values of the characteristics of socio-economic security statistics over the calculated ones calculated by models, or, on the contrary, calculated over the actual ones [2-3]. The shortest root-mean-square error is obtained from the 15th model.

Table 3.

PRELIMINARY CALCULATIONS TO IDENTIFY THE PRESENCE OF CYCLES IN A TIME SERIES OF DATA LEVELS OF SOCIO-ECONOMIC SECURITY STATISTICS

Year Model

6 13 15

- 15 0.999 0.999 0.924

- 14 1.000 1.001 0.996

- 13 1.004 1.008 1.017

- 12 1.009 1.014 1.025

- 11 0.997 1.003 1.011

- 10 0.980 0.984 0.990

-9 0.998 0.999 1.003

- 8 0.989 0.986 0.989

- 7 1.018 1.010 1.014

- 6 0.997 0.985 0.990

-5 0.986 0.971 0.976

-4 1.006 0.989 0.995

- 3 1.019 1.004 1.010

- 2 1.019 1.014 1.015

- 1 1.005 1.019 1.010

t 0.965 1.014 0.968

Source: elaboration of author.

When calculating the magnitude of the forecast error, different approaches are used. For example, the time series of data levels of socio-economic security statistics (1, ..., N) is divided into

2 parts: retrospective — p (1... K) and preemption — L (K +1,..., N). By indicators of the retrospective period the model is built Y=a_0+a_1t and represents the forecast for K+1,..., N years. Forecast errors s in K+1,..., N years is calculated as the difference between the available levels of socio-economic security statistics and the predicted ones identified by the developed model. Then at the same time one-year duration of flashbacks (I,...., K +1) and decreases the duration of the lead period (K +2, ..., N).

Again, built a predictive model and calculated forecast errors, etc. until that time, is still the period of pre-emption. The average forecast errors for each of the years of the lead period L find the means of dividing the number of errors for the year, identified by different models, but their number (for the last year of the lead s s, since for the calculation of s is applied to only one model, built 1,..., N data —1). On the basis of the obtained indicators, a forecast model is built that demonstrates the dependence of the average forecast error on 2 indicators — the size of the pre-forecast period (p) and the size of the lead (L):

£ = ^(p,L) (5)

According to the proposed model, it is possible to predetermine the average monitoring errors for the development of the lower and upper limits of the forecast version of the values of the characteristics of socio-economic security statistics. Creating a model is a labor-intensive process so that when predicting the characteristics of socio-economic security statistics, it is advisable to use, as a rule, a deterministic component of trend models.

References:

1. Frenkel, A. A. (1989). Prognozirovanie proizvoditel'nosti truda: metody i modeli. Moscow, Ekonomika, 213. (in Russian).

2. Shvaiba, D. (2018). Structural stability and socio-economic security of the hierarchical system. Bulletin of Science and Practice, 4(6), 233-239. doi:10.5281/zenodo.1289852.

3. Shvaiba, D. (2018). Socio-economic security of the hierarchical system. Bulletin of Science and Practice, 4(6), 248-254. doi:10.5281/zenodo.1289862.

Список литературы:

1. Френкель А. А. Прогнозирование производительности труда: методы и модели. М.: Экономика. 1989. 213 с.

2. Shvaiba D. Structural stability and socio-economic security of the hierarchical system // Бюллетень науки и практики. 2018. Т. 4. №6. С. 233-239. DOI: 10.5281/zenodo.1289852.

3. Shvaiba D. Socio-economic security of the hierarchical system // Бюллетень науки и практики. 2018. Т. 4. №6. С. 248-254. DOI: 10.5281/zenodo.1289862.

Работа поступила Принята к публикации

в редакцию 15.12.2018 г. 18.12.2018 г.

Ссылка для цитирования:

Shvaiba D. Trend models for the analysis of socio-economic security // Бюллетень науки и практики. 2019. Т. 5. №1. С. 258-263. Режим доступа: http://www.bulletennauki.com/38-54 (дата обращения 15.01.2019).

Cite as (APA):

Shvaiba, D. (2019). Trend models for the analysis of socio-economic security. Bulletin of Science and Practice, 5(1), 258-263. (in Russian).