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28.Вiкiпедiя. [Електронний ресурс] - Режим доступу: ИйрБ^/ик^И^ресНа.огд^И^/меметика.
29.Медведева, О.М. Корпоративна культура та культурний контекст проекту розвитку оргашзацп. Частина 1. Основы визначення [Текст]/ О.М. Медведева // Управлшня проектами та розвиток виробництва : зб. наук. пр. - Луганськ : СНУ iм. В.Даля, 2008. -№3(27). - С.96-103.
Рецензент статт! Стаття рекмоендоиана до
д.т.н., проф. Бушуев С.Д. публ1кацГ| 12.10.2015 р.
UDC [517.534]
I.I. Kovalenko, L.S. Chernova, A.S. Orekhov
COMPARATIVE ANALYSIS OF THE SHORT-TERM FORECASTING METHODS OF THE LOCALLY-HETEROGENEOUS TIME SERIES OF THE HIGH-TECH ENTERPRISE'S OPERATION INDICATORS
The article deals with monitoring technical, economic, and financial indicators of enterprise's operation using short-term forecasting methods. Here, the comparative analysis of the methods has been performed. Tabl.2, ref. 7.
Key words: short-term forecasting methods, moving average method, locally-heterogeneous time series, time series sampling
JEL O22
Setting of the problem in the general form and its link with the essential science-based or practical tasks. Modern conditions of the market economy in which high-tech enterprises exist require constant checking of the various indicators of their activity. This is achieved by monitoring, evaluation, and management of risk-contributing factors that may be present in the technical, economic, and financial results of enterprise's activity. One of the important approaches to solving this problem is a short-term forecasting of the values of these factors using well-known methods: moving average and its modifications, moving median, exponential smoothing, and others. However, these methods tend to operate stably with fixed (uniform) time series, and they are sensitive to the heterogeneous component series, i.e. we can see the appearance of bias and inefficiency average scores generated as a result of these short-term forecasting methods.
Analysis of researches and publications and selection of the unsolved parts of the general problem. Analysis of a series of publications on short-term forecasting methods [1, 2, 3, 4] revealed that a series of moving averages: simple moving average, the cumulative moving average, weighted moving average, the moving median, etc. is described and implemented currently. In [2] method of exponential smoothing - which is based on the smoothing method - the rate of decrease in the balance of a number of elements has been defined. Analysis of heterogeneous time series with the use of statistical and adaptive approaches is given in [5]. The formalization of locally-heterogenetic time series and their models are given in [6]. At the same time issues on the comparative analysis of methods of short-term forecasting of heterogeneous and locally-heterogeneous time series are described insufficiently.
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The goal of research is to compare the methods of moving average with forecasting of the values of locally-heterogeneous time series.
Here, we use probability distribution function as a value which characterizes the heterogeneous data.
Main findings. In general, a time series describes the dynamics of the technical, economic, financial, and other indicators which can be described by the class of locally-moving series in which stationary (homogeneous) and non-stationary (heterogeneous) periods follow each other. These changes cause the heterogeneity in the values of the series.
Under a heterogeneous set of data we mean one that is formed under the influence of various causes and conditions. Distribution laws of the data have a complex structure (for example, the curve of probability density can be multimodal or has so-called "fat tails"). As an indicator characterizing the heterogeneity of the data we use the probability density function F(x) and its parameter of location /. Then,
some set of data X = {x-|,X2,..., xn} ^ X^et (het means "heterogeneous") is heterogeneous if the following conditions are met:
F(X) = {fi(X),/2(X),..., fm(X)} 3 {fmod1(X),...,fmod(k)(X)}
/( x ) -/ x )| = ©;
© * 0; k > 1
or (1)
F ( X ) = {f|( X ),/2( X ),..., fm ( X )} 3
fmod ( X )
O.X) > a(x); /(x) -/€(x)| « 0.
Here, fj(x),i = 1,m is the value of function F(x) and fmody (x), j = 1,k is the modal value of the function j .
and are the theoretical and estimated value of parameter of location,
respectively (for instance, mathematical expectation and sampling mean).
© is the parameter of the values j and /^E shift a and <€€ are root-mean-square deviations.
Conditions as in (1) result in symmetrical and unsymmetrical mixtures of distributions of the following forms:
F( x) = (x; /1, CT1) + s2/2( x;/2,a2) +... + ekfk (x; Jk ak)
F( X) = ef1( x; J1,a1) + e2f2( x;/2,ct2, ©1) +... + £kfk (x; Jk, a k, © 1)'
k
where e = Y ej = 1 is the specific weight of series values which determines
j=1
each distribution fj ,
and a is the root-mean-square deviation.
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Let's define the segment Xq^q) of time series X(T) which originates in point 10 and has the length (counts number t of values Xj is carried out by the time series pattern, i.e. Xq = {x1, X2,..., Xj,..., xm }.
We can divide conventionally the sampling into the following two components:
Xi = {x(1),{x 21).....{x(1)} is the value of Xq , which determines the base of forecast
and X2 = {x(2),{x(2),..., {x(2)} is the value which determines the forecasting time
frame {Xi, X2} c Xq . Taking into account this and acting similar to formulas (1) u (2) we can examine the following time-series models:
- homogeneous time series:
F( Xq) = f (x;m,c), s = 0. (3)
- time series with locally-heterogeneous values in the forecast base X1:
f ( Xq ) = fx1 + fx2; fx1 = sf (x'; m, J) + (1 - £)f (x; m, j);
fX2 = f (x; m,j); (4)
F ( Xq ) = [sf (x'; m, c) + (1 - s)f (x; m, j)]^ + [f (x; m, j)]x2
where x' is the value of series which determines the heterogeneities in the forecast base
(x'>> x or x '<< x).
- time series with locally-heterogeneous values in the forecasting time-frame
f( xq ) = fX1 + fX 2; fx1 = f (x; m, j);
fX2 = sf (x'; m, j) + (1 - s)f (x; m, j) ; (5)
F ( Xq ) = [f (x; m, + [sf (x'; m, j) + (1 - s)f (x; m, j)]x2
- time series with alternate locally-heterogeneous segments in the whole sample of time series Xq :
F(Xq) = sh(x ' ;M1,J1) + S2f2(x ' '\M1C2) +... + skfk(x' ' ';mrJk) (6)
To examine the proposed methods of short-term forecasting on the models (3), (4), (5), and (6) we show their core. Moving-average method.
Let consider the time series of the form x1(t ),x2(t ),x3(t),..., xj (t),..., xn (t). We can obtain the forecast value of the form xn+1 in the instant of time tn+1, when we perform the following:
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Xi(t) + X2(t) + x3(t) +... + X/ (t) +... + xn (t) xf1 = xn +1 =---, (7)
where n - is the base of moving, i.e. number of previous values of the series falling into the average and xf is the forecast value of the series.
To obtain the subsequent forecast values of the series in the instant of time tn+2,tn+3,...,tn+k (k is the time-frame, i.e. number of time unit on which the forecast is conducted) we do the similar operations:
x2 (t) + x3(t) + x3(t) + ... + Xi (t) + ... + xn+i(t) x f2 = Xn+2 =-
* f3 = xn +3 =
n
xз (t) + ... + Xi (t) + ... + xn+1 (t) + xn+2 (t)
П ' (8)
y y Xn-k(t) + Xn-k +2(t) + ... + Xn-k +2(t) + Xn (t) X fk = Xn+k =---
Expressions (7) and (8) are the operations of "moving" along the time series with the base of moving n. Resulting set of forecasts {x f/},/ = 1,k is the arithmetic mean (sampled) values.
Moving median method.
The ranking of time series Xi(t),X2(t),X3(t),...,X/ (t),..., xn (t) is performed in the form X(i)(t) > X(2)(t) > X(3)(t) > ... > X(i)(t) > ... > X(n)(t), and the value xm3d is determined as per the following formula:
xmed (n) = x^n +yj, if n is odd-numbered; (9)
1
Xmed (n) = -(x{n/) + X(n/2+1)), if n is even-numbered.
2'
We take the xm3d as the quality of forecasting value. Above described technique is conducted on every step of moving within sampling value of the forecasting time-frame k.
Modified method of the moving averages with bootstrap technique of resampling. When the moving-average method is applied it is reasonable to check out the unbiasedness of sampled average and its efficiency on every step of moving. We use the bootstrap technique (resampling) [7] for this purpose. The resampling consists of the following:
We take the sampling of time series values as Xq = xi,x2,x3,...,xn which scope equals base of moving forecast n. Then, we determine the average estimation _ 1
as X = — Zn=1x/ . We exclude the element xi, from the initial sampling X0 after that
we obtain the first modified sampling Xi = x2, x3,...x/,..., xn and _* i
Xi = n^i zn=i x/.
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Then, we exclude the element from Xq and element x1 is brought back in
the sampling thus, we obtain X2 = x1,x3,...x*,...,xn and X2 =
^ ZU xi , etc.
until n modified sampling forms with the scope (n - 1) and n-estimations of sampling
— *
average X* ,i = 1,n as well.
We examine sum of squares of residual difference to determine the spread of obtained estimations X and X* :
Fq = z (x* - x )2, Fi = z (x* - xi )2, F2 = Z (x* - X2)2,..., Fn = Z (x* - xn)2 (10)
i=1
*=1
*=1
*=1
In addition, we determine the relative efficiency of the estimations (G) with use of the following expressions:
r Fq
G1 = F0 =
z (x* - x)
*=1
,G2 = ^ =
z ( x* - x )
*=1
_ 2 F
r FQ
..., Gn = = F
z (x* - x)
*=1
-.(11)
z (x* - x1 )2
*=1
z (xj - x2 )2
* =1
n
z (x* - xny *=1
Verification of the conditions when F* ^ min and G* ^ max let us obtain the average estimation with minimal value spread. This estimation has the maximal efficiency and accepted as the forecast value.
Let perform arithmetical examination of the forecast methods using data sampling which simulate the models (3), (4), (5), (6):
1. Data sampling of the homogeneous time series
J.iL L2 J-Li J'ldi -'■IS 1.6 17 J-IS
4 4 3 5 6 6 5 8 7 5 5 4 | 6 7 7 4 5 CD
X1= {x1, x2,..., x12> is the series values which compose base of forecast, l = 12
X 2= {x13, x14,..., x18} is the series values which compose the forecasting time-frame k = 6
2. Data sampling of the series with locally-heterogeneous segments in the base of forecast.
X1 = {x4,xj,x1o} cX1 is values of series which determine the heterogeneity
X.
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n
n
n
3. Data sampling of the series with locally-heterogeneous segments in the forecasting time-frame.
X2 = {x15, x1y} c X2 is the values of time series which determine the heterogeneity X 2 .
4. Data sampling of the series with locally-heterogeneous segments either in the forecast base or forecasting time-frame.
X1 = {x4,x7,x10} c X
X2 = {X15, X17} c X2
We calculate the forecast error e to estimate the forecast quality which has been obtained by the methods of short-term forecasting. We can calculate errors upon four samples with the following formula:
f
e =
1 k \Xav " 7 Z -
k j=1 xav
xf
\
• 100%,
(12)
where xav is the actual value of series; Xf is the forecasting value of series; k is the forecasting time-frame.
For interpretation of obtained errors we use values from table 1.
Standard Error Values of the Forecast and Their Interpretation
Table 1
e, (%) Interpretation
<10 High Accuracy of the Forecast
10...20 Good Accuracy
20...50 Satisfactory Accuracy
>50 Unsatisfactory Accuracy
Results of obtained calculations are listed in table 2.
Conclusions. We have obtained results of the comparative analysis of methods of the short-term forecasting upon four different types of time series. Analyzing these results we have concluded that:
- implementation of the method of moving average upon homogenous sampling of time series let obtain the high accuracy of the forecast (eMMA = 8.42) However, MMA and MM methods employed upon the same sampling have less accuracy than when MA method has been applied but accuracy of these methods is accepted as good (eMMA =20.0%; eMM =20.0%);
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Table 2
Comparison Results Methods Short-Term Forecasting
Sampling type of the time series Method of short-term forecasting Step-wise forecast errors in the forecasting time-frame (k = 6)% Total error of the forecasti ng e, (%) in the forecasti ng timeframe (k=6)
x13 x14 x15 x16 x17 x18
1. Homogeneous Moving Average (MA) 14.0 20.0 22.85 28.75 8.0 6.7 8.42
Modified Moving Average (MMA) 13.6 24.72 23.14 39.67 12.42 6.5 20.0
Moving Median (MM) 16.7 28.5 28.5 25.0 0 16.7 19.2
2. Locally-heterogeneou s in the forecasting base Moving Average (MA) 26.7 12.85 17.14 116 67.2 42.6 282.0
Modified Moving Average (MMA) 12.1 0.4 3.5 90.8 48.3 22.7 29.64
Moving Median (MM) 0 14.3 14.3 50.0 20.0 0 16.4
3. Locally-heterogeneou s in the forecasting time-frame Moving Average (MA) 16.7 25.0 68.5 38.75 62.7 7.3 36.5
Modified Moving Average (MMA) 6.88 20.72 67.0 35.0 64.9 11.8 34.41
Moving Median (MM) 16.7 28.5 70.0 25.0 67.0 16.7 37.0
4. Locally-heterogeneou s series Moving Average (MA) 26.3 12.6 52.0 116.0 44.0 42.5 48.9
Modified Moving Average (MMA) 22.7 7.0 55.1 90.6 48.8 19.3 40.6
Moving Median (MM) 0 14.3 64.7 50.0 60.0 0 31.5
- the MA method cannot be used for forecasting of series values with locally-heterogeneous data in forecast base since use of MA method results in absurd result (eMA = 282%). This result confirms the well-known statement that use of MA method is suitable when we operate the stationary time series. In addition use of MMA and MM methods results in satisfactory forecasting values of series;
- three methods give the satisfactory accuracy either upon sampling of the series with locally-heterogeneous values in forecasting time-frame or all types of sampling.
Thus, it is reasonable to use a combined implementation of the methods to make the forecast, taking into account possible existence of the different types of sampling of time series and obtained results of examination.
REFERENCES
1. Lukashin, Yu.P. (1979). Adaptivniye metody kratkosrochnogo prognozirovaniya, Moscow, Nauka, p. 432.
2. Lewis, K.D. (1986). Metody prognozirovaniya ekonomicheskikh pokazateley, Moscow, Finansy i statistika, p 132.
3. Mishulina, O.A. (2004). Statisticheckiy analiyz i obrabotka vremennykh ryadov, Moscow, MIFI, p. 180.
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4. Orlov, A.I. (2014). Komputerno-statisticheskiye metody: sostoyaniye i perspektivy, Nauchniy Zhurnal KubGAU, No.4, pp.1-18.
5. Chistyakova, A.A. (2014). Razrabotka metodov analiza neodnorodnykh ryadov dinamiki na osnovanii statisticheskikh kharakteristikh, Vostochno-Evropeyskiy zhurnal peredovykh tekhnologiy, No. 5/4, pp. 35-42.
6. Kovalenko, I.I. (2006). Netraditsionnye metody statisticheskogo analiza dannykh, Nikolayev, Ilion, p.106.
7. Efron, B. (1988). Netraditsionnye metody mnogomernogo statisticheskogo analiza, Moscow, Finansy i statistika, p. 262.
,-, Стаття рекмоендована до
Рецензент статт _ " ... " "
4 , п ,п публ1каци 21.10.2015 р.
д.е.н., проф. Петрова 1.Л. ' ^ г
УДК 658.012.32:658.012.23
Н.Ю. Ровинская
ВОЗДЕЙСТВИЕ ОРГАНИЗАЦИОННЫХ ИЗМЕНЕНИЙ НА БИЗНЕС-МОДЕЛЬ КОМПАНИИ
Работа посвящена исследованию в области организационных изменений с целью выявления их взаимосвязи с понятием бизнес-модель. Найдена взаимосвязь ранее независимых параметров функционирования компании. Доказано воздействие организационных изменений на бизнес-модель компании и разработана модель диагностики воздействия организационных изменений на бизнес-модель. Рис. 6, табл. 4, ист. 15.
Ключевые слова: организационные изменения, бизнес-модель, модели организационных изменений, методы управления.
JELM110
Постановка проблемы в общем виде и ее связь с важными научными и практическими задачами. На сегодняшний день практически невозможно выделить сектор человеческой деятельности, который не зависит от высокой динамики внешний среды. Это утверждение обусловлено многочисленными факторами: изменениями в законодательной базе, в геополитической обстановке, в системе налогообложения, в модификациях покупательского поведения и спроса, ростом инноваций и т.д. Быстротечные вариации во внешней среде оказывают влияние на внутренние условия функционирования организации. Так предприятия вынуждены прибегать к реструктуризации, технологическим и организационным преобразованиям, созданию новых рабочих мест, трансформации нематериальных характеристик бизнеса и т.д.
Учитывая вышеописанные условия экономической деятельности, становится очевидным, что для долгосрочной и успешной работы на одном из этапов жизненного цикла компания нуждается в проведении изменений. Масштаб, интенсивность и ориентация изменений индивидуальны для каждого конкретного случая, однако многочисленные исследования в данной области свидетельствуют о том, что управление организационными изменениями вызывают не меньше сложностей, чем управление материальными составляющими бизнеса.
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