East European Scientific Journal Wschodnioeuropejskie

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East European Scientific Journal Wschodnioeuropejskie
East European Scientific Journal
Wschodnioeuropejskie Czasopismo Naukowe
#7, 2016 czqsc 4
Wschodnioeuropejskie Czasopismo Naukowe
(Warszawa, Polska)
Czasopism o jest zarejestrow ane i publikowane w Polsce. W czasopismie publikowane
artykuty ze wszystkich dziedzin
naukowych. Czasopismo publikowane jest w j^zyku polskim, angielskim, niemieckim i rosyjskim.
Artvkutv przvim ow ane sa do dnia 30 kazdeeo m iesiaca.
Czestotliwosc: 12 wvdari rocznie.
Format - A4. kolorow v druk
W szvstkie artvkutv sa recenzowane
Kazdv autor otrzvm uie ieden bezptatnv eezem plarz czasopism a.
Bezptatnv dostep do wersii elektronicznei czasopism a.
East European Scientific Journal
(Warsaw, Poland)
The journal is registered and published in Poland.
Articles in all spheres of sciences are published in the journal. Journal is published in English, German, Polish and Russian.
Articles are accepted till the 30th day of each month.
Periodicity: 12 issues per year.
Format - A4. color printing
Aii articles are reviewed
Each author receives one free printed copy of the journal
Free access to the electronic version of journal
Zespoi redakcyjny
Redaktor naczelny - Adam Barczuk
Mikotaj W isniew ski
Szym on Andrzejew ski
Dom inik Makowski
Pawet Lew andowski
Rada naukowa
Adam Nowicki (U niw ersytet W arszaw ski)
Michat Adam czyk (Instytut Stosunköw Mi^dzynarodowych)
Peter Cohan (Princeton University)
M ateusz Jabtonski (Politechnika Krakowska im. Tadeusza Kosciuszki)
Piotr M ichalak (U niw ersytet W arszaw ski)
Jerzy Czarnecki (Uniw ersytet Jagiellonski)
Kolub Frennen (University of Tübingen)
Bartosz W ysocki (Instytut Stosunkow M iqdzynarodow ych)
Patrick O'Connell (Paris IV Sorbonne)
Maciej Kaczm arczyk (U niw ersytet W arszaw ski)
Dawid Kow alik (Politechnika Krakow ska im. Tadeusza Kosciuszki)
Peter Clarkw ood(U niversity College London)
Igor Dziedzic (Polska Akadem ia Nauk)
Alexander Klimek (Polska Akadem ia Nauk)
Alexander Rogowski (Uniw ersytet Jagiellonski)
Kehan Schreiner(Hebrew University)
Bartosz M azurkiew icz (Politechnika Krakowska im. Tadeusza Kosciuszki)
Anthony M averick(Bar-Ilan University)
Mikotaj Zukowski (Uniw ersytet W arszaw ski)
Mateusz Marszaiek (Uniw ersytet Jagiellonski)
Szymon
Matysiak (Polska Akadem ia Nauk)
Michal Niew iadom ski (Instytut Stosunköw Mi^dzynarodowych)
Redaktor naczelny - Adam Barczuk
1000 kopii.
W ydrukow ano w «Aleje Jerozolimskie 85/21, 02-001 Warszawa, Polska»
W schodnioeuropejskie Czasopism o Naukowe
Aleje Jerozolim skie 85/21, 02-001 Warszawa, Polska
E-mail: info@ eesa-journal.com , http://eesa-journal.com /
Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) # 7, 2016
Сербов H. Г.
ИННОВАЦИИ В РАЗВИТИИ ЭКОНОМИКО-ЭКОЛОГИЧЕСКИХ СИСТЕМ ВОДНЫХ БАССЕЙНОВ УКРАИНЫ:
МЕТОДИЧЕСКИЕ ПОДХОДЫ И ЭКОНОМИЧЕСКАЯ ОЦЕНКА.............................................................................................. 93
Скорик Г. /., Тревого О. I.
ПРОБЛЕМИ ДЕРЖАВНОЇ ПІДТРИМКИ МАЛОГО БІЗНЕСУ ТА ШЛЯХИ IX ВИРІШЕННЯ..................................................... 96
Христина Снігур
УПРАВЛІННЯ В СТИЛІ «КОУЧИНГ» - СУЧАСНИЙ ІНСТРУМЕНТ ПІДВИЩЕННЯ ЕФЕКТИВНОСТІ БІЗНЕС-ПРОЦЕСІВ
КОМПАНІЇ............................................................................................................................................................................... 101
Фоузи Абдугадер Халоал
ЗАТРАТЫ НА ПОДГОТОВКУ КАДРОВ ВОЕННОСЛУЖАЩИХ КАК ОБЪЕКТ УЧЕТА В БЮДЖЕТНОЙ СФЕРЕ: УКРАИНА И
ЛИВИЯ - СРАВНИТЕЛЬНЫЙ АСПЕКТ..................................................................................................................................106
Nataliya Chernova, Olga Polyakova
DIAGNOSIS AND FORECASTING ECONOMY STATE WITH HIDDEN MARKOV MODEL....................................................... 112
Штогрин Г. C.
ЕКОЛОГО-ЕКОНОМІЧНІ ПРОБЛЕМИ ФУНКЦІОНУВАННЯ ЖИТЛОВО-КОМУНАЛЬНОГО ГОСПОДАРСТВА УКРАЇНИ В
КОНТЕКСТІ СТАЛОГО РОЗВИТКУ.......................................................................................................................................117
ЮДИНА И.Н.
ЧТО МЕШАЕТ ЭКОНОМИЧЕСКОМУ РОСТУ: РАЗМЫШЛЕНИЯ И ПРЕДОСТОРЕЖЕНИЯ................................................ 121
Зеркин Д. Г.
ОСНОВЫ ФОРМИРОВАНИЯ АДАПТИВНО-СИТУАЦИОННОГО УПРАВЛЕНИЯ ДЕЯТЕЛЬНОСТЮ ОРГАНИЗАЦИИ В
СОВРЕМЕННЫХ УСЛОВИЯХ..........................................................................................................'.................................. 125
Золотова Л. В., Портнова Л. В.
СТАТИСТИЧЕСКИЙ АНАЛИЗ ПОКАЗАТЕЛЕЙ, ХАРАКТЕРИЗУЮЩИХ УСЛОВИЯ ЖИЗНИ ДОМОХОЗЯЙСТВ РОССИИ И
ИХ ФИНАНСОВОЕ ПОЛОЖЕНИЕ....................................................................................................................................... 134
Черкашнев Р. Ю., Чернышова О. H., Федорова А. Ю.
РАСЧЕТ СВОБОДНОГО ДЕНЕЖНОГО ПОТОКА И ЕГО ЭКОНОМИЧЕСКОЕ ПОНИМАНИЕ..............................................139
NAUKI PRAWNE | ЮРИДИЧЕСКИЕ НАУКИ
Irena Dirgeliene
THE ASPECTS OF THE DEBTOR AND THE THIRD PARTY ACTING IN BAD FAITH - APPLICATION OF ACTIO PAULIANA IN
LAW VARIOUS COUNTRIES.................................................................................................................................................144
Irena Dirgeliene
THE PRINCIPLE OF GOOD FAITH IN DIFFERENT LEGAL SYSTEMS: COMPARATIVE ASPECTS OF THE APPLICATION 148
Витовская E. C.
ОБЩЕСТВЕННАЯ ОПАСНОСТЬ ЛИЧНОСТИ НАРКОПРЕСТУПНИКА............................................................................... 153
Гоицай И.О.
ОБЕСПЕЧЕНИИ ПОЛИТИЧЕСКИХ ПРАВ И СВОБОД ЧЕЛОВЕКА И ГРАЖДАНИНА В УКРАИНЕ В КОНТЕКСТЕ
ГЕНДЕРНОГО ПАРИТЕТА....................................................................................................................................................156
Жуковська Г. Г.
ВЗАЄМОДІЯ ОРГАНІВ ВЛАДИ ТА ГРОМАДСЬКОСТІ У СФЕРІ ПРОТИДІЇ ЛЮДЬМИ: ДОСВІД КРАЇН ЄВРОПИ................. 161
Тогузакова Д Ищанова Г. Т.
КОРРУПЦИЯ И СТРАНЫ ЕАЭС В БОРЬБЕ С НЕЙ.............................................................................................................. 168
Павлов И. E., Магдеева К. Р., Павлова С. А.
ПРАВОВАЯ ОХРАНА ЗАПОВЕДНИКОВ................................................................................................................................173
Тинистанова С. С.
АКТУАЛЬНЫЕ ПРОБЛЕМЫ ИССЛЕДОВАНИЯ ПОЧЕРКА ПОДОЗРЕВАЕМЫХ.................................................. '............ 175
Чурикова С. Д.
ПРОБЛЕМЫ ЗАЩИТЫ ПРАВ СВИДЕТЕЛЕЙ В РОССИЙСКОЙ ФЕДЕРАЦИИ..................................................................... 178
Стеиіич Е. С., Корецкий Д. А.
ТЕОРЕТИЧЕСКИЕ И ПРАКТИЧЕСКИЕ ПРОБЛЕМЫ РАЗГРАНИЧЕНИЯ НЕОСТОРОЖНОСТИ И КОСВЕННОГО УМЫСЛА
В ПРЕСТУПЛЕНИЯХ, СВЯЗАННЫХ С УБИЙСТВОМ...............
............................................................180
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u biudzhetnykh ustanovakh [Planning, accounting, reporting,
control of budgetary institutions] : navch. posibnyk / V. T.
Aleksandrov. — K. : AVT ltd, 2004. - 387 p.
12. Londarenko O. O. Ekonom ichna pryroda vydatkiv
ta ii vplyv na oblikovo-analitychni aspekty biudzhetnykh
ustanov [The economic nature of spending and its impact on
accounting and analytical aspects of budgetary institutions] /
0 . O. Londarenko // Ekonomika. Finansy. Pravo. - 2008. - №
9. - pp. 15-19.
13. Atamas P. J. Osnovy obliku v biudzhetnykh
orhanizatsiiakh
[Basis o f accounting
in
budgetary
organizations], Navch. posibnyk / P. J. Atamas. - K. : - Tsentr
navchal’noi literatury, 2002. - 284 p.
14. Biudzhetnyj kodeks Ukrainy [Budget Code of Ukraine]
vid 08.07.2010 № 2456-VI [iz zminamy ta dopovnenniamy]
[Elektronnyj resurs] // Verkhovna Rada Ukrainy [sajt], Rezhym dostupu : http://zakon3.rada.gov.ua/laws/show/2456-
17.
15. Svirko S. V. Bukhhalters’kyj oblik u biudzhetnykh
ustanovakh: m etodolohiia ta orhanizatsiia [Accounting in
budgetary institutions: m ethodology and organization] :
m onohrafiia / S. V. Svirko. - K.: KNEU, 2006. - 244 p.
16. Svirko S. V. Deiaki pytannia suchasnoi ukrains’koi
ekonomichnoi term inolohii / S. V. Svirko // Problemy
formuvannia rynkovoi ekonomiky. - Vyp. 9. - K. : KNEU. -
2 0 0 1 .- p p . 4 6 3 -4 7 3 .
17. Mykhajlov M. H., Telehun M. I., Slavkova O. P.
Bukhhalters’kyj oblik u biudzhetnykh ustanovakh [Accounting
in budgetary institutions], Navchal’nyj posibnyk. / M. H.
Mykhajlov, M. I. Telehun’, O. P. Slavkova - K.: Tsentr uchbovoi
literatury, 2011. - 384 p.
18. Natsional’ne polozhennia (standart) bukhhalters’koho
obliku v derzhavnom u sektori 135 “Vytraty” [The national
situation (standard) accounting in the public sector 135
“Expenses”] : Nakaz Ministerstva finansiv Ukrainy vid
18.05.2012 r. N« 568. [Elektronnyj resurs] // Verkhovna Rada
Ukrainy [sajt]. - Rezhym dostupu : http://zakon2.rada.gov.ua/
laws/show/z0903 -12.
19. Pro zatverdzhennia Poriadku rozrakhunku vytrat,
pov’iazanykh z utrym anniam kursantiv u vyschykh
navchal’nykh zakladakh [On approval of the calculation of
the costs associated with the maintenance o f students in
higher education] : Spil’nyj nakaz MOU, M inisterstva finansiv
Ukrainy, Ministerstva vnutrishnikh sprav Ukrainy, Ministerstva
transportu i zv’iazku Ukrainy, Administratsii derzhavnoi
prykordonnoi sluzhby Ukrainy, upravlinnia Derzhavnoi
okhorony Ukrainy, Sluzhby Bezpeky Ukrainy vid 16 lypnia
2007 r. № 419/831/240/605/537/219/534. - [Elektronnyj
resurs]. // Verkhovna Rada Ukrainy [sajt]. - Rezhym dostupu:
http://zakon3.rada.gov.ua/laws/show/z0863-07.
DIAGNOSIS AND FO RECA STING EC O N O M Y STATE W IT H H ID D E N MARKOV
M O D EL
Nataliya Chernova,
Sim on K uznets K harkov N ational University o f Economics, Ukraine,
Ph.D., Associate Professor o f the D epartm ent o f Econom ic Cybernetics.
Olga Polyakova,
Research centre o f industrial developm ent problem s o f N A S o f Ukraine,
Ph.D., C hief o f the D epartm ent o f Innovation D evelopm ent a n d Competitiveness
ABSTRAC T
IThe article is aim ed to forecast the fu tu r e states o f econom y basing on restricted inform ation about its banking subsystem. V ie
key hypothesis assumes that state o f an economic system m ay be interpreted as a hidden variable. Using several banking indicators
as observable variables it is possible to fo r m H idden M arkov models. For know n sequence o f each observed variable values the
appropriate sequence o f state classes is determ ined. The results obtained fo r all observed variables are aggregated to fo r m the optim al
sequence o f state classes. The initial models are adjusted due to Baum -W elch algorithm. Then fu tu r e states o f econom y as precrisis ones
are determ ined basing on absolute probabilities.
Key words: banking system, state o f economy, observed variables, hidden m arkov model, forecasting.
I. INTRODUCTION
The global financial crisis has affected banking systems of
many countries and has perform ed exactly as banking crisis,
However, there is the controversial tendency in fact too. Total
system crisis courses financial resources decline both firms
and households for. This process stimulates capital flight from
banks and landing decrease.
That is why models of rising and spreading crisis have
made an interest in scientific world last years. Most of them
are devoted to early warning systems and safety criteria for
economy [1-2]. Nevertheless assessments of banking system
inlluence on the economy during crisis period are very rare
ones
So the main aim of the paper is to determ ine the state class
of economy basing on banking system variables.
-
Let’s assume that each state
may be changed at the
beginning of the m onth and is stable during the month. The
num ber of states is finite. That is why the process of changing
states may be defined as stochastic discrete process,
The initial set of states may be divided into separate
jg
g
g \
hom ogeneous classes * 1 ’ 2 ’" -’ 1
Let’s assume that
the probability of a certain class of state at time t depends on
the class of state at time (t-1 ) only. That is why the process of
changing classes may be defined as stochastic discrete Markov
process.
State class is not observable directly. That is why the
sequence of classes is hidden, unobserved to the researcher. We
can only determ ine the certain value of “state class” indicator
indirectly using set o f observed and measurable indexes. Here
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Wschodnioeuropeiskie Czasopismo Naukowe (East European Scientific Journal) \ EKONIMIA # 7, 2016
we suggest that banking subsystem indexes have to be used as
observable ones. The value o f each observed banking index
depends on the state class of the economy.
Hence, such situation may be represented by Hidden
Markov Model (HMM).
Initially HM M was im plem ented into technical sphere
for solving speech recognition problems [3-4]. However, the
modal has become applicable for diagnosis and forecasting
some econom ic processes. The most part of such applications
is dedicated to stock markets researches [5]. However, there
are lots of examples o f HMM successful employment in other
spheres. For instance, R. S. M am on and R. J. Elliott suggest
using HM M when studying volatility in growth rate of real GDP
and inflation [5]. Authors [6] use hidden m arkov models in
custom er relationships dynamics research. Some demography
problem s are studied in [7]. H um an mobility modelling is the
object of study in [8]. From the other hand, H M M is not widely
used as forecasting tool for the complex economic systems
behaviour.
II. RESEARCH SET UP
Each H M M consists o f two types of variables:
hidden variable, which is not directly observable (let it
be class of the state o f the economy);
variable, which is observable and measurable (let it be
one of banking subsystem indexes).
The following notation m a y b e used to describe HMM [34]:
A = (P,B,w)
P'j L/L ,
probability distribution,
L- num ber of classes;
B = {bl(Jc)}
M
■
(4)
'flie m atrix B is estim ated according to the formulas below:
Iw
b,{k) = — ------, k = l , M
s
j = [1, L\
k = [\,M]
|1 . % = K ,
w
0, otherwise.
3(0 = m a x P(q„q2,--.,ql =Sl, 0 v 0 2,...,0l \ A)
(7)
8 t (i)
m axim um probability that for the given first
t values o f the observed variable the sequence of classes is
finished in the i-th class at the time t.
Step 2. Initialization
- num ber of unique values of observed variable,
8 I( i ) = w ib , ( O l ) i = [ 1 , L ]
V i(i) ~ 0
To form transition matrix P
(9)
Step 3. Recursion
firstly we need to estimate
G = (gU)- ,
4U) =max l S J O P t W
)
1<i<L
{1)
( 10)
T
w. i j ) = arg max[^,,(0^]
= I
1<i<L
(2)
class, U
(8)
initial class of the state probability
frequency matrix
g
(6)
To explore HMM effectively three following problems can
be solved:
for certain sequence o f observed variable values
determ ine the probability that the sequence is generated by the
HMM;
for certain sequence o f observed variable values
determ ine the appropriate optimal sequence of state classes;
for certain sequence o f observed variable values adjust
the HM M to maximize the probability that the sequence is
generated by the HMM.
This work is dedicated to the last two problems.
The second problem is solved by Viterbi algorithm, which is
represented below [3-5].
Step 1.D eterm ine additional variables.
distribution.
%
=
- observed
probability of k-th value of observed variable for
w = (w|,w 2,...,w L)
(5)
s - num ber o f states in the i-th class,
Vk - the k-th unique value for the observed variable,
9 , 9 , ,
class j,
M
I.
_ c[ass 0f jhg state transition
variable probability distribution,
bj{k)
Si,
P'j = —
-transition frequency from the i-th class to the j-th
j = [LL]
t = [2,T ]
do
Step 4.Termination
= [! ,/,],
1, X t_, - S, AX, = S j5
p
=max[<5r (/)]
1<i<L
0, othewise.
(3)
Finally, transition probabilities must be estim ated as follows:
qT
=argmax[<Sr (z)]
1<i<L
-
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( 13)
Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) \ EKONIMIA # 7, 2016
Step 5.State sequence backtracking
q, = y y l+, ( q , + i )
j
=
t
(14)
- i,t
The third problem is solved with Baum-Welch algorithm
[3-4]:
Step 1. D eterm ine additional variables.
£( i’J) = P ( q , = Si,qt+i = Sj\
probability o f a path being in class
O.X) _
the
§.
1 at time t and making
a transition to class >+ ' at time t + 1, given the observation
O
\
sequence w and the model /Vl.
<
pt (i) = P(qt
= S (|\ 0 , X )7
Tn x
' 11
being in class
O
S-1
u kk,. f
- the probability of
at tim e t, given the observation sequence
and the model ^ .
(pt( i ) = %J,(Uj)
Then
Step 2. Parameters reestimation.
W i=<Pl(i).
--------
PiJ
5>,t/)
t =i
b / ( k ) = — 1^
—
X <?,(./)
/=1
IV. CALCULATION
We studied the dynamics of Ukrainian economy in
2006-first half 2015(monthly data) [9].
Each state o f economy is described as a point in the
m ultidim ensional space
X t ~ ( x i i > x t 2 ’ ■■■’ x p )
p - num ber of indicators, that describe a state.
To form the classes of states we used such indicators as:
industrial production index,
volume o f agriculture product,
volume o f construction output,
custom er price index,
industrial producer price index,
monthly average wages and salaries,
registered unemployment,
load o f registered unemployed per 1 vacant work
place.
As the banking subsystem indicators we used:
loans granted by depository corporations (except
National Bank o f Ukraine)
loans of households,
consum er loans,
loans for house purchase.
To form HM M we need to solve the following problem:
how to take into account all possible values of the observed
variable and to guarantee:
the completeness o f the observations set
not very large value o f variable .
We suggest to use growth rates of observed variables and
to convert initial discrete tim e series into interval ones. So, lets
interpret as the num ber o f intervals of observed variable.
According to the cluster analysis algorithms three
hom ogenous groups o f economy states were formed. The
first group consists of states which represent 2006-2007 years,
February 2008, 2011-2012 years, January-February 2013;
the second group contains 2009 year and 2015(first half),
the rem ained states form the third group. O ur suggestion is
to interpret the first group as comparatively stable class, the
second - as crisis class, the third - as precrisis class.
Transition m atrix P for three classes is represented below
(see formulas (1) - (4)).
Table 1
Transition matrix
Classes
Comparatively stable
Precrisis
Crisis
Comparatively stable
0,94
0,06
0,00
Precrisis
0,04
0,91
0,04
Crisis
0,00
0,06
0,94
M atrix B was calculated for each observed variable
according to formulas (5)-(6). Matrixes are represented below
(tables 2-5).
-
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Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) \ EKON1MIA # 7, 2016 _______________________
Table 2
Matrix Bj for loans granted by depository corporations
Intervals
VB1(
V“1,
V B1,
v B1d
<0,84
|0,84;0,92)
(0,92; 1,00)
1,00=<
comparatively stable
0,00
0,00
0,54
0,46
precrisis
0,07
0,13
0,58
0,22
crisis
0,06
0,11
0,72
0,11
Classes
Table 3
M atrix B, for loans of households
Intervals
yB2
yB2
yB2
VB2
<0,92
[0,92;0,98)
[0,98; 1,05)
1,05<
comparatively stable
0,00
0,00
0,56
0,44
precrisis
0,11
0,13
0,69
0,07
crisis
0,06
0,28
0,67
0,00
Classes
Table 4
M atrix B3 for consum er loans
Intervals
Classes
y tu
VB\
V“3
V“\
<0,85
[0,85;0,93)
[0,93; 1,01)
1,01 <
0,50
comparatively stable
0,00
0,00
0,50
precrisis
0,02
0,11
0,60
0,27
crisis
0,06
0,06
0,83
0,06
Table 5
M atrix B4 for loans for house purchase
Intervals
v Mt
VM
<0,92
[0,92; 1,00)
V B4
•
[ 1,00; 1,08)
comparatively stable
0,00
0,46
0,32
0,22
precrisis
0,04
0,69
0,24
0,02
crisis
0,11
0,56
0,28
0,06
Classes
Thus, we have obtained four HMM, which have the
com m on m atrix P and vector w, but different matrixes B.
Viterbi algorithm was applied to each H M M to determ ine
the optimal sequence of economy classes for period jan-jun
1,08<
2015.
Observed variables values for period Jul-Dec 2015 are
shown below,
Table 5
G rowth rates of observed variables
Period
loans granted by depository
corporations
loans of households
consum er loans
loans for house purchase
July 2015
0,98
0,98
0,97
0,99
August 2015
1,00
0,99
1,00
0,98
September 2015
0,95
0,86
0,82
0,93
O ctober 2015
1,03
1,02
1,01
1,04
November 2015
0,96
0,96
0,95
0,99
D ecember 2015
0,94
0,95
0,95
0,96
Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) \ EKONIMIA # 7, 2016
According to the inform ation about discrete intervals
(Table 2 - Table 5) the appropriate sequences o f observed
intervals were determ ined. These sequences are used as inputs
for Viterbi algorithm (Table 6).
Table 6
Sequences of observed intervals
Period
loans granted by depository
corporations
v B]2
v B14
v*
July 2015
August 2015
September 2015
loans o f households
yB2
3
yB2
...............
VB2
.
V »2
O ctober 2015
,3
November 2015
W B1
yB 2
December 2015
v B13
3
V »2
_____ V _ 2 —
All models have determ ined the crisis class o f economy
during the second half o f the 2015 yeap.
To verify these results k-m eans procedure was used to
form hom ogenous sets o f states for the period 2006-2015. 'lhe
results correspond with those obtained by Viterby algorithm.
Baum-Welch algorithm was applied to adjust initial four
hidden markov models. As the result four new transition
P. Pi Pi
P4
matrixes were obtained:
1 , L , J and
H.
'these matrixes were used to estimate four variants of
absolute probabilities of each class (comparatively stable,
precrisis, crisis) at the first six m onths o f the current 2016 year:
g k i= w { P ky t
R ki
- vector of absolute probabilities for the j-th m onth for
the k-th model,
£ e r 1; 4]
- index o f the particular hidden markov model,
/ e [1; 6]
- m onths index,
^
- initial vector o f absolute probabilities.
To calculate the final average absolute probabilities for the
j-th m onth the following formula was used:
z : = \ ± z k;
^ k=\
g-i
1
j-th m onth,
-average absolute probability of the i-th class for
' - absolute probability of the i-th class for the j-th m onth
according to the k-th model.
Finally, the following absolute probabilities were obtained
for the first six m onths o f the 2016 year:
g = (0; 0,25; 0,75).
VI. CONCLUSION
O btained results allow to sum up that Hidden Markov
Models may be used to identify the future class of states of
consum er loans
v«
VB3
2
V“\
VB3
VB\
VB
3
______2____
loans for house
purchase
yB 4
yB i
2
ym
yB 4
yB 4
VB4
economic system based on current banking system variables,
th e advantage o f this approach is the possibility to estimate
the state of economy using restricted initial inform ation. Ihe
accuracy of the assessment increases thanks for using several
models based on different observed variables. Four models that
were formed by loans granted by depository corporations, loans
o f households, consum er loans and loans for house purchase
have dem onstrated corresponding results.
According to the models the Ukrainian econom y deepened
into crisis at the first h alf of 2016. Future research should be
concerned to including crisis indicators from other economy
subsystems as predictors to the model.
VII. REFERENCES
1. E.P. Davis, D. Karim, Com paring early warning systems
for banking crises. Journal of Financial Stability. 4, 2 (2008)
89-120.
2. S. Percic, C.-M. Apostoaie, V. Cocri§, Early warning
systems for financial crises - a critical approach, CES Working
Papers. 1 (2013) 78-88.
3. L. Rabiner and B. Juang, “Fundamentals of Speech
Recognition," Prentice-Hall, Englewood Cliffs,NJ, 1993.
4. L.R Rabiner, “A tutorial on HMM and Selected
Applications in Speech Recognition,” In:[W L],proceedings of
the IEEE, Vol. 77 (2), pp. 267-296,1993.
5. R. S. M amon and R. J. Elliott, editors. H idden Markov
Models in Finance. International Series in O perations Research
& Management Science. Springer-Verlag, New York, 2007.
the
6. Netzer, Oded, James Lattin, and V. Srinivasan. «A
H idden Markov Model of C ustom er Relationship Dynamics.»
M arketing Science 27, no. 2 (M arch 2008): 185-204.
7. Gilbert Ritschard, Michel Oris, Dealing with Life Course
Data in Demography: Statistical and Data M ining Approaches
(h ttp ://m e p h is to .u n ig e .c h /p u b /p u b lic a tio n s /g r/rits _ o ris _
m ining_dem ohist.pdf).
8. Ha Yoon Song Application o f H idden Markov Model
for H um an Mobility Modelling (http://w w w .naun.org/m ain/
N AU N /com puters/2007-113.pdf).
9. State Statistics Service of Ukraine docum ents publishing
(http://ukrstat.org).
-U&-
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Zespöt redakcyjny
Redaktor naczelny - Adam Barczuk
Mikotaj W isniewski
Szymon Andrzejewski
Dom inik M akowski
Pawet Lewandowski
Rada naukowa
Adam Nowicki (Uniwersytet Warszawski)
Michaf Adam czyk (Instytut Stosunköw M i^dzynarodowych)
Peter Cohan (Princeton University)
Mateusz Jabtonski (Politechnika Krakowska im. Tadeusza Kosciuszki)
Piotr M ichalak (Uniwersytet Warszawski)
Jerzy Czarnecki (Uniwersytet Jagiellonski)
Kolub Frennen (University of Tübingen)
Bartosz W ysocki (Instytut Stosunköw M i^dzynarodowych)
Patrick O'Connell (Paris IV Sorbonne)
Maciej Kaczmarczyk (Uniwersytet Warszawski)
Dawid Kowalik (Politechnika Krakowska im. Tadeusza Kosciuszki)
Peter Clarkw ood(University College London)
Igor Dziedzic (Polska Akadem ia Nauk)
Alexander Klim ek (Polska Akadem ia Nauk)
Alexander Rogowski (Uniwersytet Jagiellonski)
Kehan Schreiner(Hebrew University)
Bartosz M azurkiewicz (Politechnika Krakowska im. Tadeusza Kosciuszki)
Anthony M averick(Bar-llan University)
Mikofaj Zukowski (Uniwersytet W arszawski)
Mateusz Marszatek (Uniwersytet Jagiellonski)
Szymon M atysiak (Polska Akadem ia Nauk)
Michat Niewiadom ski (Instytut Stosunköw M i^dzynarodowych)
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