modeling of the investment and construction ......construction trend in russia inna nikolaevna...

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 8, Issue 10, October 2017, pp. 1432–1447, Article ID: IJCIET_08_10_145

Available online at http://http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=8&IType=10

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

© IAEME Publication Scopus Indexed

MODELING OF THE INVESTMENT AND

CONSTRUCTION TREND IN RUSSIA

Inna Nikolaevna Geraskina

St. Petersburg State University of Architecture and Civil Engineering,

Russia, 190005, Petersburg, 2-nd Krasnoarmeiskaya St., 4

Andrey Vladimirovich Zatonskiy

Perm National Research Polytechnic University, Russian Federation, 614990,

Perm, 29 Komsomolsky prospekt

Alexander Alekseevich Petrov

St. Petersburg State University of Architecture and Civil Engineering,

Russia, 190005, Petersburg, 2-nd Krasnoarmeiskaya St., 4

ABSTRACT

The research results are especially relevant under conditions of the current systemic

cyclical crisis caused by the change long waves of economic development and

technological structures. Such processes have the ability to generate a new order, not

forced by the exogenous force but having a spontaneous character as a result of the

endogenous factors transformation. The fluctuations occurring in the socio-economic

environment, instead of fading, are amplifying, and the socio-economic system develops

in the direction of arbitrary self-organization. Taking into account the fact that

complicated self-organized systems cannot be imposed with the way for their

development, new approaches are required to trend forecasting and system management

taking into account natural patterns and properties revealed in the process of economic

and mathematical modeling. This allows shifting the bifurcation diagram at a certain

period of time, bypassing the system critical point which leads to an undesirable

outcome. Timely and qualitative forecasting of crisis points, administrative effects

modeling with the purpose of transition to a new favorable way of the economic system

development is reasonable and justifiable. Since there are compelling reasons to regard

the investment and construction sphere of Russia as a field of the synergistic patterns

action and its evolution cyclical nature revealed, the trend can be set with a certain

degree of accuracy by the differential equation systems, which allows identifying existing

alternatives of system behavior and obtaining more complete information about the

future. The article presents a new approach to the modeling and evolution forecasting of

complex cyclic and stochastic economic systems. Based on the qualitative and

Modeling of the Investment and Construction Trend in Russia


quantitative analysis of the Russian investment and construction industry statistical data

the main order parameters and system control variables are identified. A model is

developed, which is based on a second-order differential equation that makes it possible

to use statistical data and forecast in the long term the system behavior depending on

managerial effects. The dynamics is identified of the control variables impact on system

order parameter within different time periods.

Key words: investments, construction, modeling, prediction, development.

Cite this Article: Inna Nikolaevna Geraskina, Andrey Vladimirovich Zatonskiy and

Alexander Alekseevich Petrov, Modeling of the Investment and Construction Trend in

Russia, International Journal of Civil Engineering and Technology, 8(10), 2017, pp.

1432–1447.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=8&IType=10

1. INTRODUCTION

Under the conditions when the Russian economic system, with a shortage of financial resources,

is experiencing an acute need for innovative and structural modernization of a number of

important economic spheres, including investment and construction, it is necessary to develop

complex programs and projects that promote system self-organization at the minimal costs for

modeling and future forecasting. For that end it is important:

– to posses a reliable and complete information regarding trends status of the economic system;

– to define the system regularities, features, indicators, which characterize to a greater extent

(phase parameters) the scope of the economic activity and variables having a significant impact

on them (control parameters).

Investment and construction activities are one of the priority areas of the national economy

and they make a significant contribution (about 5.5%) to the national macroeconomic indicators

growth. Despite this, the scientists examine it without a detailed understanding of the

development immanent properties and patterns as a complex self-regulating system. The

strategic task for the nearest future is to search for objective ways to manage this subsystem

focusing towards achieving the self-organization and sustainable development.

In terms of system approach, the investment and construction field (ICF) of Russia is a

complex and multifaceted subject of scientific research, one of the most important self-regulating

subsystems of the national economy representing an organized set of structural elements with

nonlinear connections that have independence in choosing the optimal operation mode, focus

towards the cost-effective activities and satisfaction of public needs for construction sites, and

having the synergistic systems properties. The latter include: the plurality of dissimilar entities

and relationships between them (transactional links, ownership schemes); the presence of non-

linear relationships that lead to the emergence of relatively stable structures; the integration and

coherent processes; high adaptive ability for turbulent environmental conditions and interference;

the systemic relations are of the organized nature at most; the entities integration is carried out on

the basis of direct, reverse and reserve links; the cyclic path dependency, etc. [1].

Inna Nikolaevna Geraskina, Andrey Vladimirovich Zatonskiy and Alexander Alekseevich Petrov


2. METHOD

The traditions of modern factorial and regression analysis are such that, as a rule, the economic-

mathematical models are placed on algebraic polynomials when building the linear multifactor

models (LMM). In case of dynamic models developing the formula 1 is used:

0 i ii

y t y x t a a x t , and more often

0n i i ni

y t a a x t , (1)

where t – arbitrary point of time,

tn – time of the next values counting in the series of factors.

Such models are interpreted in a simplified manner, approximately as follows: investing in an

enterprise according to the diagram x1(t), allows obtaining a pure discounted income (or another

economic performance indicator) ) )) taking into account the market requirements to

the products (disturbance) z1(t). At that, it is assumed a priori that there is only a linear

relationship between the factors and system response value, and the only dynamic element in the

model is the time lag Δt. Similar approaches are used in doctoral dissertations [2; 3; 4], where it

is assumed by default that there are only direct links between factors and reaction force, and the

only dynamic element is a delay. For example, in models of the type (formula 2):

( ⃗ )) ∑ ) (2)

This assumption is unjustified. According to the general philosophical reasoning it follows

that the application of force always leads to a change in certain process acceleration, Newton

second law at least. In this regard, it would be logical to put the differential equation of the type

(formula 3) as the basis of the model [5]:

2

2

1d x tF t

mdt

, (3)

The "forces" here should be the values of factors (control variables).

For complex systems, such as ICF, the regression identification of coherence between y(t)

and xi(t) without convincing evidence of their mutual independence leads to the pointlessness of

modeling and forecasting. The same results bring up an attempt to extrapolate values y(t)

according to the time series data, including with the use of autoregressive models.

The research results [6; 7; 8; 9; 10] develop the ideas of the economic systems modeling

using the regression-differential equation. The latter can reconstruct the oscillation and cyclic

transient processes without additional mathematical efforts (identification and exclusion of the

periodic process, trend, etc.), the possibility of the response value output to the asymptote, which

is typical for many objects, including economic systems. This can not be taken into account in

LMM.

In order to determine the outlines of ICF economic-mathematical model, it is necessary to

perform the regression analysis, as well as to determine the form and order of the differential

equation. It is important to get a fairly simple tool for ICF trend forecasting, where there is no



any problem with data identification, but lacking LMM disadvantages. The use of the 1st order

ordinary differential equation (ODE) in the model leads to a high prediction error and a piecewise

broken trend in the partial approximation of factors integration, derivative values jumps, which is

infeasible based on ICF properties.

Regression-differential modeling (RDM) provides a reliable coincidence of the first and

second derivatives of reaction values series. This means the following: if the original series

increases with slowdown, then the segment obtained by post prognosis will also grow with a

slowdown, although it may "overrun" and "lag" behind the original series. Forecasting based on

RDM is not yet free of shortcomings and ambiguities. For example, one has to use the trial-and-

error method, gradually including and excluding factors, and observing the change in the total

root-mean-square deviation of the model throughout all the initial data series, or within the

horizon of post-forecast.

Thus, the construction of RDM of n-order has the following form (formula 4):

1

01 1

2

1 1 1

n in m

i i i in ii i

m m m

ij i i j j i i ii j i

d y t d y tg a b y t c x t

dt dt

d x t x t f x t

, (4)

where ig – the influence coefficients of reaction lower derivatives, a – the constant

describing effect of one n-derivative of the reaction in constructing a trend, b – the feedback

factor describing the reaction value impact on its own n-derivative, ic – factors influence

coefficient, :ijd i j – factors mutual influence coefficient, i iif d – factors square influence

coefficient, i – lag of i-factor, 0 – lag in the feed back, is produced by the sequential inclusion

in it of a series of factors and refusal to include the factor if it worsens the error of the model.

RDM is complemented by the n-1st initial condition:

'0

0dyy

dt

, 2

''02

0d yy

dt , … ,

1

1

01

0n

n

n

d yy

dt

.

The unknown variables in this case are all the initial conditions, and also: 0'y , a, b, ci, dij, fi,

0, i. Their search is performed by minimizing the criterion, that is, by solving the minimization

problem:

0 0

0 0

' , , , , , , , :

: ' , , , , , , , min

i ij i i

i ij i i

y a b c d f

S y a b c d f

In particular, if we do not take lags into account, we obtain for the second-order RDM

(formula 5):



2

21

2

1 1 1

m

i ii

m m m

ij i j i ii j i

d y t dy tg a b y t c x t

dtdt

d x t x t f x t

(5)

Search for the unknown variables is performed by minimizing the criterion (formula 6)

2

исх1

K

k kk

S y t y t

(6)

computed value root-mean-square deviation y t from the reaction series statistical values

исх ky t , that is, solve the minimization problem (formula 7):

0 0 0 0' , , , , , , , : ' , , , , , , , mini ij i i i ij i iy a b c d f S y a b c d f (7)

To exclude the influence of dimensions, the series of factors are preliminarily normalized to

an interval [0, 1] by the formula 8:

min

max min

i k i kk

i ki k i k

kk

x t x t

x tx t x t

(8)

The reactions series is normalized in a similar way. Technically, the minimization can be

performed in MatLAB or Mapl environment.

3. RESULTS

3.1. The Analysis of the Dynamics of the Main Statistical Indicators

The dynamics analysis of the basic statistical indicators [11] and graphical representation of their

time series in the form of phase curves, allowed considering that the only possible ICF operation

mode is cyclic dynamics with a trend towards cycle time reduction (table 1, figure 1, figure 2)

[12]. The system had three cycles within a period from 1990 to 2016, indicated in figure 1 with a

dotted line. The reasons for this trend are identified: exogenous factors that take into account the

fluctuation effects of higher-order economic systems, and the endogenous mechanism of

parameters cyclic behavior associated with variable and control parameters nonlinear interaction.

This confirms the presence in the phase space of an attractor with a significant attraction force.

Herewith, the system space dimensionality reduction occurs, and ICF development can be

described with a small number of statistical parameters, since they will represent the process

sufficiently complete with an enormous set of variables.



Table 1 Scope of work performed in the investment and construction field in billion rubles and

commissioning of buildings, structures, individual production facilities, houses, social and cultural

facilities in Russian Federation, million square meters, 1990 - 2016

Year

Projects

commissioning,

mln m2

Scope of work,

RUB bn Year

Projects

commissioning, mln

m2

Scope of work,

RUB bn

Value Index Value Index Value Index Value Index

1990 61.7 - 0.1 - 2004 60.0 1.1 1313.6 1.26

1991 49.4 0.8 20.5 168.0 2005 66.3 1.1 1754.4 1.34

1992 41.5 0.8 50.2 2.5 2006 75.6 1.1 2350.8 1.34

1993 41.8 1.0 58.7 1.2 2007 98.1 1.3 3293.3 1.40

1994 39.2 0.9 80.5 1.4 2008 102.5 1.0 4528.1 1.40

1995 41.0 1.0 153.7 1.9 2009 95.1 0.9 3998.3 0.88

1996 34.3 0.8 225.8 1.5 2010 91.5 0.9 4454.1 1.11

1997 32.7 0.9 242.6 1.1 2011 99.0 1.1 5140.3 1.15

1998 40.8 1.2 240.9 1.0 2012 110.4 1.1 5714.1 1.11

1999 42.1 1.0 329.9 1.4 2013 117.8 1.1 6019.5 1.05

2000 44.7 1.0 558.5 0.8 2014 138.6 1.2 6125.2 1.02

2001 47.7 1.0 703.8 0.9 2015 139.4 1.0 5945.5 0.97

2002 49.6 1.0 831.0 1.2 2016 130.2 0.9 5749.4 0.97

2003 53.7 1.1 1042.7 1.3

Figure 1 Phase curve of the rate of volume of work executed by kind of economic activity "construction"

in 1998 – 2015



Figure 2 The phase curve of the index amounts entered in the action of buildings,buildings, separate

production facilities, houses, objects socially-cultural appointment in 1990 – 2016

The obtained results are necessary for the economic and mathematical modeling of ICF

subsequent and effective management [13; 14; 15; 16; 5]. The model should be based on a

differential equation of the second and higher orders to account for the cyclic and oscillatory

processes. The management accounting for the synergetic features and economic and

mathematical modeling results allows shifting the bifurcation diagram at a certain period of time,

bypassing the critical point which leads to an adverse outcome [17; 18].

3.2. Modeling

As ICF order parameter the authors selected a statistical quantitative indicator – "Commissioning

of buildings, structures, individual production facilities, houses, social and cultural facilities"

measured in thousands of square meters, which characterizes to the maximum extent the system

development dynamics. An analysis of the set of ICF statistical indicators made it possible to

distinguish the control variables (tab. 2).

Table 2 Control variables and their designation

Designation Control variable

Х1 Investment in equity, mln. RUB (Before 1998 – RUB bn).

Х2 Volume of real estate loan, RUB bn

Х3 Expenses per RUB 1, works, kop.

Х4 Population of the RSFSR/RF, people

Х5 Average monthly wages of workers in construction organizations, RUB, in thousands

Х6 Overall construction materials production index

Х7 Consolidated price index for the main types of construction materials and works

Х8 Average per capita incomes of the population, RUB per month (before 1998 RUB, in

thousand)

Х9 Provision of own resources of construction organizations

Х10 Share of expenses for the acquisition of real estate in the monetary expenditures of the

population



Х11 Refinancing rate, %

Х12 Annual inflation in the Russian Federation,%

Х13 Volume of housing construction, thousand square meters.

Х14 Productivity index

Х15 Level of construction profitability, %

Х16 Average prices of 1 square meter of the total area at the primary housing market, RUB.

Х17 Availability of fixed assets, RUB bn

Х18 Number of operating construction organizations, pcs.

The entire modeling interval was divided into three segments corresponding to significant

changes in the social and economic system of the USSR and the Russian Federation: 1) 1990 –

1998; 2) 1999 – 2007; 3) 2008 – 2016 ICF RDM was built according to three time periods. RDM

diagram for the period of 1990 – 1998 (before denomination) is shown in Figure 3.

Benchmark data Post-prognosis for 6 years

Post-prognosis for 7

years Resulting model

Figure 3 RDM period 1990 – 1998

Since a smooth curve is the solution of differential equations of high orders which does not

have discontinuities of lower derivatives, the approximation of the order parameter was

performed by a cubic spline, and control variables between the annual counting were

approximated linearly. The forecast trends for this period were obtained through gradual increase

in the number of years. Factors with low-valued coefficients were discarded until their

elimination began to lead to a sharp increase in the error. The factors remaining in the model

have the coefficients presented in the final model (table 3).

Obviously, a decrease in ICF indicators for 1996 – 1997 is successfully predicted using

RDM, even according to the 1990 – 1994 data, but with a significant error. The addition of the

following years to the model leads to the post-forecast adjustment, and according to the 6-year

data it turns out to be satisfactory.



Table 3 RDM factors weight

Factor Х1 Х2 Х3 Х4 Х5 Х6 Х7 Х9 Х10 Х11 Х12 Х15 Х16 Х17

Final factors weight for RDM 1990 – 1998.

Ci 16.

86 0

66.2

1

-

20.03 0 -3.6 6.88 2.95

-

57.9

16.1

8 5.44

-

12.33 0

-

48.79

Initial factors weight for RDM 1999 – 2008.

Ci

-

0.2

4

-

0.37 -0.12 0.07 1.37 0

-

0.08 0.04 0.11 -0.05

-

0.04 0.04

-

0.42 0.46

Weights of RDM factors in 1999 – 2008 after the first factors exclusion

Ci

-

0.3

5

-

0.38 -0.13 0 1.21 0

-

0.08 0 0.11 0 0 0

-

0.38 0.30

Final weights of RDM factors in 1999 – 2008 after exclusion of factor Х7

Ci 0.2

6

-

0.19 -0.12 0 1.54 0 0 0 0.11 0 0 0

-

0.40 0.37

Initial factors weight for RDM 2008 – 2016.

Ci

-

0.0

1

-

0.10 0.17 0.03

-

0.11

-

0.02 0.08

-

0.12 0.12 -0.1

-

0.05 -0.75 0.02 0.23

Weights of RDM factors in 2008 – 2016 after the first factors exclusion

Ci 0 -

0.11 0.19 0

-

0.15 0 0.08

-

0.09 0.12 -0.09

-

0.05 -0.85 0 0.26

Final weights of RDM factors in 1999 – 2008 after exclusion of factor Х12

Ci 0 -

0.07 0.25 0

-

0.18 0 0.05

-

0.07 0.11 -0.09 0 -0.83 0 0.30

Neither model is capable of forecasting beyond 1998, which is considered absolutely normal.

Models built according to 6 – 8 years show to varying degrees the growth in the commissioning

of construction projects, which can be referred to as a way out of the crisis of 1994-1996. Based

on the signs and absolute values of the weight coefficients for factors in RDM (table 3) we can

draw the following conclusions: the paramount importance for ICF development in recent years,

covered by the model, can be attributed to factor Х3 (expenses per RUB 1, works, kop.). Its

dynamics according to the years covered by RDM is shown in Figure 4.

Figure 4 Dynamics of factor Х3 RDM 1990 – 1998



By the time of the financial crisis it became clear to a certain circle of ICF entities that it is

more profitable to increase construction costs and this process began to develop non-linearly.

"Share of expenses for the acquisition of real estate in the monetary expenditures of the

population" factor had the biggest deterrent effect. This is quite logical – the poorer the

population and the greater the proportion of all available funds belongs to the forced purchase of

real estate, the more difficult is to sell the constructed housing on the market.

In this case, it is difficult to estimate the presence of the current dynamics, that by 1998 the

population became more active in purchasing real estate than few years earlier. The lack of funds

ceased to be a deterrent for making a decision on investing in real estate. It is interesting that Х9

factor interpreted as "the force that affects ICF" acquired in around 2006 has a positive and

steadily growing importance. This indicates that ICF by this factor was restrained by 1998, and

its growth (more precisely, its acceleration) has already become positive. Construction

enterprises provided with their own fixed assets, began to accelerate the construction growth

rate. This is a good example illustrating the fundamental difference between the explanatory

properties of LMM and RDM.

Similarly, we have built RDM according to the data of 1999 – 2008 adding 2010 and 2011 to

control changes in the object of research. The post-forecasts obtained are given in Figure 5. The

model, constructed according to the data of 1999 – 2005 qualitatively forecasts the trend

inflection in 2008 – 2009, but not its consequences.

Benchmark data

Post-prognosis for 6 years


Resulting model


Figure 5 RDM and post-forecasts of 1999 – 2008

The study results allowed considering that the conditions for 2008 financial crisis had

developed a few years before it and provoked this negative synergetic effect. Post-forecast

fluctuations in the "plus" and "minus" compared to the initial data indicate the fluctuations in

ICF properties and structure during this period.

Table 3 shows that the factors Х4, Х6, Х9, Х11, Х12, Х15 have weight coefficients with an

absolute value of less than 5% of the maximum value according to coefficient module. We



eliminate them from the model, identify the coefficients and growth of the approximation error.

It increased from 0.01248 to 0.02046, and the qualitative nature of the forecasted trends

remained the same: in 2008 the post-forecast quality reduces, but not as much as it was in 1998

model. The reduction in the approximation error is not significant, it shows that factors exclusion

from the model is justified. The weight of Х7 factor is sufficiently small, which indicates the

possibility of excluding it from the model. All the models confidently forecast ICF reaction drop-

down after 2008 and, of course, do not account for its change as a result of 2008 crisis.

Therefore, its post-forecast is unsatisfactory.

The maximum positive effect on ICF dynamics is associated with Х5 factor X5 (average

monthly wages of workers in construction organizations), which is quite easy to explain. The

following factor, which has a positive effect on ICF trend is Х17 factor (availability of fixed

assets), which changed the sign in comparison with the past period model. These weight

coefficients are stable and do not change significantly in models built up according to the data

before 2005, 2006, etc. The largest deterrent effect on ICF dynamics is caused by Х16 factor

(average prices of 1 square meter of the total area at the primary housing market), which also

does not need comments. Further, we built RDM corresponding to the period of 2008 – 2016.

(Figure 6).

Figure 6 RDM and post-forecasts of 2008-2016

The quality of RDM post-forecasting draws a special attention. They, according to the data of

2008 – 2011 and 2008 – 2012 are almost identical and do not coincide with reality, although

forecast a certain inflection of the trend around 2014 with subsequent sharp drop-down.

Probably, something has changed within these years essentially in the series of factors, which

resulted in delay in the drop-down and further peak shift in time, since the post-forecast for 6

years almost exactly coincides with the original data, and adding two more annual counts does

not change much. The model approximation error is 0.1012.

3.3. Identification of Factor Models

According to the absolute values of Х1, Х4, Х6, Х16 factors weight less than 5% of the maximum,

therefore we excluded them from RDM and found new coefficients. The approximation error has



decreased two-fold and is 0.06886. The nature of post-forecasts has not changed, the "jump" in

the transition to 6 years has been preserved. It is reasonable to exclude the only Х12 factor from

RDM, since its weight is 5.5% of the maximum. We obtained the final RDM (Figure 7). The

forecast error has slightly increased and is 0.08651. Trends nature has not changed.

Figure 7 RDM post-forecast in 2008-2016 after Х12 factor exclusion

Let us analyze the dynamics of the factors weights with an increase in the number of years

for ICF post-forecast construction (table 4), by dividing them into three groups: 1) the factor

weight is changing smoothly with an increase in the number of years when constructing the post-

forecast; 2) the factor weight is changing step by step, taking into account the 6-year series when

constructing the post-forecast; 3) the factor weight is not changing in any number of the post-

forecast years.

Table 4 RDM factors weights for the period of 2008 – 2016 according to the corresponding post-forecast

years

Post-forecast, years Х2 Х3 Х5 Х7 Х9 Х10 Х11 Х15 Х17

4 (year 2012) -0.0797 0.2248 -0.1681 0.0821 -0.0904 0.1232 -0.0999 -0.955 0.3109

5 (year 2013) -0.0870 0.2248 -0.1691 0.0821 -0.0894 0.1232 -0.0999 -0.9545 0.3110

6 (year 2014) -0.0700 0.2452 -0.1803 0.0539 -0.0657 0.1089 -0.0900 -0.8363 0.2970

7 (year 2015) -0.0690 0.2452 -0.1803 0.0539 -0.0658 0.1089 -0.0901 -0.8327 0.2970

Entire model -0.11 0.2452 -0.1803 0.0539 -0.0659 0.1089 -0.0902 -0.8289 0.2970

Group 1 2 2 2 2 2 3 1 2

% Change - 9.1% 6.6% 34.3% 26.5% 11.6% - - 4.5%

The greatest change between 2013 and 2014 is attributed to ICF driving forces – Х7 and Х9

factors. Both the factors weights have decreased in absolute terms: Х7 – began to accelerate

construction to a less extent, Х9 – slows it down to a less extent. It should be noted that this

change occurred quickly and "stepwise". RDM factors values for the three periods are shown in

Table 5.



Table 5 RDM factors values for all periods

Period Х1 Х2 Х3 Х4 Х5 Х6 Х7

1990 16.8609 0 66.2121 -20.0299 0 -3.5669 6.8762

1998 0.2597 -0.188 -0.1174 0 1.5403 0 0

2008 0 -0.068 0.2452 0 -0.1803 0 0.0539

Factors values in proportions of the maximum factor weight module

1990 25.5% 100.0% -30.3% -5.4% 10.4%

1998 16.9% -12.2% -7.6% 100.0%

2008 -8.2% 29.6% -21.8% 6.5%

Period Х9 Х10 Х11 Х12 Х15 Х16 Х17

1990 2.9513 -57.9116 16.1808 5.4366 -12.330 0 -48.785

1998 0 0.106 0 0 0 -0.3985 0.3753

2008 -0.0659 0.1089 -0.0902 0 -0.8289 0 0.297

Factors values in proportions of the maximum factor weight module

1990 4.5% -87.5% 24.4% 8.2% -18.6% -73.7%

1998 6.9% -25.9% 24.4%

2008 -8.0% 13.1% -10.9% -100.0% 35.8%

4. DISCUSSION

It is interesting to note the following patterns of changes in ICF RDM factors weights that turned

out to be significant in the models of all the periods:

1. Х10 factor impeded the construction growth during the Soviet period, and began to accelerate

somewhat during the post-crisis period;

2. The same is true for Х17. As soon as the Soviet economic model collapsed, this factor became

one of the main factors in ICF development [19; 20; 21].

3. Х1 factor accelerated the construction significantly during the Soviet period and before 2008

crisis, and then its significance decreased.

4. Х3 and Х5factors, although they do not correlate with each other in a linear term, have a clear

negative correlation as construction driving forces. They are probably interchangeable to some

extent in RDM (with different signs), but, unfortunately, no RDM well-developed analytical

theory exists.

5. During the Soviet era, perhaps because of the deep comprehensive ties of the planned

economy, large number of construction driving forces was significant. In a market economy, the

fewer driving forces are of importance, while the rest are negligibly small.

In order to forecast ICF development we should consider the change in the normalized values

of the factors in recent years (Figure 8).



Figure 8 The factors normalized values dynamics in 2012-2016

It can be seen from the diagrams that the factors values have no pronounced linear or

quadratic trends, so, their values forecasting for the next years is difficult. However, their series

values can not be independent, therefore, it is reasonable to assume that the series can be

approximated with some self-similarity model (a model in the state space) when the next state of

the external environment, that is, the value of the factor vector at the next time reference is not

random, but depends on the previous state (formula 9):

1k kx t a Bx t , (9)

where В – transition matrix, а – initial state vector, tk - k-th count of the series in time.

Having determined the parameters а and В by the least squares method, we will obtain a fairly

good reproduction of factors (sum of quadratic deviations for 2012 – 2016. S = 1.42*10-12

. Through

re-calculations in the following years we have obtained RDM factors forecast (table 6).

Table 6 ICF RDM factors forecast values 2017-2019

Factor 2012 2013 2014 2015 2016 2017 2018 2019

Х2 0.5398 0.7400 0.9917 0.6128 1.0000 0.8567 0.2371 0.7400

Х3 0.0000 1.0000 1.0000 0.8000 1.0000 0.9041 0.3621 1.0000

Х5 0.8656 1.0000 0.9892 0.6344 0.6398 0.5274 0.4134 1.0000

Х7 0.1143 0.0000 0.0857 0.2229 0.0857 0.1655 -0.0211 0.000

Х9 0.5649 0.6183 0.6565 1.0000 0.7328 0.8915 0.1849 0.6183

Х10 0.4787 0.4681 0.1596 0.9255 0.8830 1.0787 0.0906 0.4681

Х11 0.0952 0.0952 0.0952 0.0952 0.4286 0.3716 -0.0063 0.0952

Х15 0.1750 1.0000 0.3500 0.1250 0.0500 -0.1107 0.5063 1.0000

Х17 0.6554 0.7124 0.9164 0.9663 1.0000 1.0426 0.2046 0.7124

Y 0.3946 0.5491 0.9833 1.0000 0.8079 0.5237 0.4591 -0.0021



5. CONCLUSIONS

Thus, the research showed that currently ICF dynamics can be described with a few statistical

parameters, since the system moves near the attractor and dimensionality of its space is reduced,

and the selected parameters subspaces in the phase space quite fully represent everything that

occurs in an enormous set of variables.

ICF development cyclical nature predetermines the inexpediency of using LMM to forecast

the dynamics and consequences of control impacts due to: system complexity, stochasticity,

inertness, consistency, presence of oscillation transient processes, nonlinear links between

factors and reaction dynamics, high values of the mean square errors.

Forecast ICF RDM factors values indicate that if the control variables dynamics will be

subject to the same patterns as before 2016, then ICF in 2017 will face a decrease in the resulting

indicators. This trend will not change practically in 2018, and in 2019 the moment will come of

ICF stability loss when it reaches the values of 2010 resulting indicators.

In order to maintain ICF stable trend and avoid an undesirable forecast zone, a complex of

management decisions is required, aimed at: immanent factors activation of the economic system

and combined effect of control variables that have a certain degree of impact. ICF trend

withdrawal from the negative forecasts zone by influencing the values dynamics of the control

variables will be identified as a type of synergistic effect "sustainable development".

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