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com hekim tr

A comparison of ANFIS and ARIMA techniques in the forecasting of electric energy consumption
of Tokat province in Turkey
A comparison of ANFIS and ARIMA
techniques in the forecasting of electric energy
consumption of Tokat province in Turkey
Rüstü YAYAR
Faculty of Economics and Administrative Science
Gaziosmanpasa University, Tokat, Turkey
[email protected]
Mahmut HEKIM
Tokat Vocational School
Gaziosmanpasa University, Tokat, Turkey
[email protected]
Veysel YILMAZ
Suşehri Timur Karabal Vocational School
Cumhuriyet University, Sivas, Turkey
[email protected]
Fehim BAKIRCI
Faculty of Economics and Administrative Science
Atatürk University, Erzurum, Turkey
[email protected]
Abstr ct
In this study, the electric energy demand of Tokat province was estimated by means of
ANFIS and ARIMA techniques. Seven different forecasting experiments were implemented for the subscriber groups and the consumption of electric energy which is the
dependent variable. The electric energy demand of the province for the first six months
of the year 2011 was estimated by means of ANFIS and ARIMA techniques. The
obtained results were compared and interpreted in order to illustrate the forecasting
success of these techniques. We showed that the ANFIS is more appropriate than the
ARIMA in point of the forecasting of electric consumption.
Keywords: Electric energy consumption, Forecasting, ANFIS, ARIMA, and Tokat.
Jel odes: C22, C45, Q47
Volume 1
Number 2
July 2011
87
Rüstü YAYAR & Mahmut HEKIM & Veysel YILMAZ & Fehim BAKIRCI
Introduction
Nowadays, energy is an important source of life. By entering into the life of mankind in 1880s, the electric energy gradually became an indispensable part of modern
life and industry (Şekerci Öztura, 2007).
In order to generate the electric energy, which is a secondary energy source, the
support of primary energy sources is needed. Electric energy is widely used in many
fields, and a large part of energy resources for the benefit of the people are converted
into electric energy (Demir, 1968). The electric energy demand has been continuously increasing in parallel with the growing population, urbanization, industrialization, technologic deployment, and enhancement of welfare.
The spread of the usage fields of electric energy which is one of the most important
parts of all types of economic activities increases the electric energy demand. Also,
since the distribution network provided a great deal of the electric energy of even the
smallest residential areas, the share of electric energy in the total energy consumption increased (Kılıç, 2006).
The province of Tokat is geographically located between 39-51, 40-55 North latitudes and 35-27, 37-39 East longitudes, in the inner side of middle Black Sea part
of Black Sea Region. Covering the 1.3% of mainland Turkey, elevation from the sea
level of the province is 623m and surface area of it is 9.958km² (Governorship of
Tokat, 2006). There are 12 districts of Tokat province including with the central district¹. Historical periods of the province consist of Hattie, Hittite, Phrygian, Med,
Persian, Alexander the Great, Roman, Byzantine, Arabian, Danishmend, Anatolian
Seljuk, Mongolian, Ilkhanid, Ottoman Governments and Emperors (Provincial
Department of Environment And Foresty of The Governorship of Tokat, 2007:1).
The province of Tokat became a province with the proclamation of the republic in
1923 (Turkish Statistical Institute, 2010:10). By 2010 the population of the province is 550.703 (Turkish Statistical Institute, 2010).
The province has a wide potential of both agriculture and other sectors (such as tourism). In the economic structure of the industry, agriculture, livestock sector plays
an important role. Particularly in the food industry, rock and land-based industries,
forest products industry and in recent years, textile weaving and garment sector is
the backbone of the economy in Tokat (Provincial Department of Environment
And Foresty of The Governorship of Tokat, 2007:130).
88
Journal of Economic and Social Studies
Electric energy was firstly provided in the city center of Tokat in 1935 by the Hydroelectric power plant which was built on Aksu for the city lightening. This power
plant consists of 2 tribunes with 175 horsepower (HP), and each tribune operates
by 230 m³ water passing through the water channel. The power plant provided
electric energy of 135 kWh for 1580 subscribers. However, the electricity production was insufficient for the city. Because of Almus Hydroelectric power plant
built in 1966, Tokat had continuously the electric energy, and still it provides the
electric energy of the city. Besides, transmission lines were renewed and electric energy of every part of the city was provided by using 18 transformers (Governorship
of Tokat, 2006). The installed power plant in Tokat consists of Almus, Köklüce,
Ataköy Hydroelectric power plants within Tokat. Almus Hydroelectric power plant
became operational in 1966 and Number of Unit – Power is 3X9 MW and its
installed power is 27 MWAnnual production of the plant is 100 GWh. Köklüce
entered service in 1998 and Number of Unit – Power is 2X46 MW and its installed
Power is 90 MW. Annual production of the power plant is 588 GWh (Electricity
Generation Corporation, 2011). The construction of Ataköy Hydroelectric power
plant dam was completed in 1977. Having 5.5 MW Power, its annual production is
8 GWh (VIII. Regional Directorate of State Hydraulic Works, 2011).
In this study, electric energy demand are estimated by Adaptive Neuro-Fuzzy
Inference System (ANFIS) and Autoregressive Integrated Moving Average (ARIMA)
techniques by using the electric energy consumption data of Tokat province in the
time of period between January 2002 and December 2010. Matlab 7.04 package
program is used for the ANFIS model and Minitab 14.0 package program is used
for the ARIMA model.
Aim
This study aims at contributing to the planning of supply by estimating electric
demand in the future. The demand for electric energy was forecasted in Tokat province by means of the ANFIS and the ARIMA models. The generation planning of
electric energy is very important because it cannot be stored, and therefore must be
consumed shortly after its generation. If these kind local studies were generalized
into all country, it helps the supply planning and provides a more effective usage
of resources. Therefore we estimated the electric energy demand by ANFIS and
ARIMA models for Tokat province.
Volume 1
Number 2
July 2011
89
Literature
Energy consumption and demand are among the most debated topics, and many
studies have been made available in the literature. It is seen that the studies especially
focused on the causality between the electricity consumption and economic growth
and controversial results has been achieved. There are scarcely any studies on electric energy consumption and demand through ANFIS and ARIMA models. These
models are often used in engineering studies.
There are many studies in various fields by using the fuzzy logic method. In one of
them, Tufan and Hamarat (2003) analyzed the “Aggregation of The Financial Ratios
of publicly-traded companies Through Fuzzy Logic Method”.
The first detailed study examining the demand for electricity with the help of econometric models is the work of Houthakker (1951). The study includes the econometric analysis of the household electricity demand through cross-section data from
the period of 1937-1938 for 42 residential center in England. Another study was
conducted by Fisher and Kaysen. Fisher and Kaysen (1962) using time-series and
cross sectional data, examined the demand for electricity with the help of multiple
regression and analysis of covariance. Electric demand was taken up in four components, including electricity demand, household electricity demand, industrial electricity demand and the short and long period determinant of them. Accordingly,
short run is in question if the stock of electric appliances is fixed and long run is in
question if the stock is variable. In the case of industry, short run is in question if
there is an assumption that technology is invariable and long run is in question if
there is an assumption that technology is variable (Tak, 2002).
Al-Garni and Javeed Nizami (1995) developed a model of artificial neural networks
for electric energy consumption with the data from seven years such as temperature,
moisture, solar radiation and population. After the comparison of the model of
artificial neural networks with the regression model, it was revealed the model of
artificial neural networks was a better forecasting model.
Al-Garni and Abdel-Aal (1997) estimated the Electric Energy consumption for five
years on the east of Saudi Arabia for the consumption on the sixth year, developing monthly ARIMA models by using the univariate and Box-Jenkins time-series
analysis. When ARIMA models are compared to the abductive network machinelearning models, it is seen that ARIMA models needs less data and coefficient and
give better results as well.
90
Brown and Koomey (2002) examined the increase in electric demand in their work
named “Electric Use in California: Past Trends and Present Usage Patterns. They
took sector (settlement, commercial, industrial, agricultural and other) of electric
consumption from the previous period as data. They brought forward that there
had been a great increase in the electric demand in 1990, compared to 1980 and
that it stems from the increase in buildings and the tendencies in the building sector
(Enduse Forecasting and Market Assessment, 2011).
It can be seen that the studies on the modeling of the energy consumption and demand, which is also crucial for the economy of Turkey, accelerated in 2000s. There
are not many studies, done widely on the provincial (regional) electricity consumption and demand. State institutions and organizations of which subject of activity
is electricity became obliged to state the electricity consumption of the provinces
on their annual report on the basis of subscriber groups after “Legislation On The
Annual Reports Drawn Up By The Public Administrations” were published by the
Ministry of Finance on the Official Gazette dated 17.03.2006 and became effective on 01.01.2006 (Official Gazette, 2006). These institutions conduct studies also
on the monthly and yearly electric data which must be sent to Turkish Statistical
Institute (TÜİK) and Ministry of Energy and Natural Resources (ETKB) by these
institutions even though these data changes in the ensuing years.
In the work of Terzi (1998) which analyzes the relationship between the electric
consumption and economical growth for the period of 1950-1991, the relationship between the electricity consumption and of the commerce house, industry and
household and economical growth; the long period relationship between the variables were determined through the Engle-Granger cointegration method and the
short run dynamics were analyzed through the debugging tool. It was determined
through this econometric method that the income and price elasticity were in fact
inelastic. A meaningful and two-way relationship between electricity consumption
and economical growth came along in the business and industry sector.
Sarı and Soytaş (2004) employed the technique of generalized forecast error variance
decomposition and came to the conclusion that the electricity demand and variance
in national income growth are as important as employment (Lise & Van Monfort,
2005).
Çebi and Kutay (2004) used artificial neural networks while estimating the long run
electric energy consumption and compared the results to the Box-Jenkins models
and regression technique. The results revealed that using artificial neural networks
was a good forecasting method for electric energy consumption.
Volume 1
Number 2
July 2011
91
In addition, we must specify the MAED (Model for Analysis of Energy Demand)
model study of Ministry of Energy and Natural Resources, the most important
study that was conducted in our country, which reveals the medium and long run
general energy demand and electric energy demand in this demand.
Research Method
In this study, monthly electricity consumption data of Tokat province was used.
This data covers the period between January 2002 and December 2010. The subscriber groups consist of private houses, industry, business firms, government agencies and other subscribers. The total electricity used in agricultural irrigation, fresh
water, work-sites, temporary activities, state-owned enterprises, municipalities, internal activities, prefectures, sanctuaries, and local government lightening systems
was also included in these groups. Seven different experiments were implemented
for investigating the success of the ANFIS and the ARIMA models in the forecasting
of the total electric energy consumption of all subscriber groups.
Time Series and Box-Jenkins Forecasting Model
Time Series
A time series is simply a sequence of numbers collected in regular intervals (as day,
month and year) over a period of time (Dikmen, 2009: 227). Time series monitors
the motion of a variable in a time sequence. For example, monthly unemployment
ratio, monthly increase ratio of money supply, annual inflation ratio, monthly electric use, etc. Time series can be also used as a resource of knowledge acquisition
and a method for forecasting the future. While in the evaluation process, analysis is
important in degrading the trend, growth trend, seasonality, cyclical, and irregular
fluctuations (Bozkurt, 2007). The selection of method used for forecasting the future values depends on the estimation of purpose, type and elements of time series,
amount of data, and the length of the estimation period (Asilkan & Irmak, 2009).
92
Box-Jenkins Forecasting Model
Box-Jenkins method is the most widely used model for stationary time series modeling. For the implementation of Box- Jenkins method, the time series must be
stationary (with constant mean, variance and autocorrelation). If the series is not
stationary, it should be made stationary by taking the difference of a few times
(Gujarati, 2009).
Box-Jenkins method is based on the principle that each time series is a function of
past values and may only be explained by means of them. Some assumptions cannot
be applied based on the econometric models, but there is not any restrictive assumption for Box-Jenkins method (Bircan & Karagöz, 2003). In this method;
• In contrast to the regression models that explain yt with a k number of explanatory variables of x1, x2, x3,…, xk,
• The dependent variable Yt can be explained by its own past or lagged values and
stochastic error terms.
The most important stage of the Box-Jenkins method is the selection of the appropriate ARMA (p, q) model by examining the autocorrelation and partial autocorrelation coefficients. Experience of the researcher is very important because of this
phase is not able to determine mechanically. If the time series is not stationary,
artificial autocorrelations will prevent the model to determine. Non-stationary time
series is transformed stationary time series by logarithmic transform or taking differences.
Autocorrelation and partial autocorrelation coefficients of the distribution can be
examined with the help of graphs (autocorrelation function (ACF) and partial autocorrelation function (PACF). When the autocorrelation coefficients are seen to
be approaching zero exponentially, AR model must be applied; while the partial
autocorrelation coefficients are realized to be approaching the same level mentioned
above, then MA model must be used; if both of these approach zero exponentially;
ARMA model must be applied in this situation.
In ARMA model, the degree of AR is determined by the number of partial autocorrelation coefficients (p), while the degree of MA is determined by the number of
autocorrelation coefficients (q) (Önder & Hasgül, 2009: 65–66).
Volume 1
Number 2
July 2011
93
(PACF).
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pthe
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ation, coefficients
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Y1t past
Φ
Φ
Y
2
Φ
Φ
1
2
t

t

2
at
is
the
error
term.
In In
thethe
above
model,
, Y,t 1 ,...,
is
the
values
of
past
observation,
,
,...,
ispΦthethe
1Φ
2Φ
Y
Y
above
model,
,...,
is
the
values
of
past
observation,
,
,...,
t

p
theterm.
above model,
, t 2 ,...,
is the values of past observation, 1 , 2 ,..., isp is
th
e and at is the In
error
δ is
δ
Y
Φ
MA(q)
Model
coefficients
forfor
thethe
values
of
past
observation,
the
constant
value
and
at
is
the
error
term.
Y
Y
MA(q)
Model
Φ
Φ
coefficients
values
of
past
observation,
is
the
constant
value
and
at
is
the
error
term.
t

p
p
1 , t  2 ,...,
1 , at2 ,...,
In the
above model,
is the valuesδofis past
observation,
is theterm
coefficients
for the tvalues
of past observation,
the constant
value and
is the error
δ is the constant value and at is the error term.
Model
coefficients
for
the
values
past
observation,
In MA
(q)MA(q)
model,
Yt value
isofthe
linear
function
of average
pastpast
errorerror
terms
in qinperiod
MA(q)
Model
In
MA
(q)
model,
Y value
is the
linear
function
of average
terms
q period
MA(q)
Model
MA(q)
Model t
backwards.
MA
(q
)
model
is
shown
as
follows:
backwards.
MA
(q
)
model
is
shown
as
follows:
error terms
in In
qModel
period
MA (q) model, Yt value is the linear function of average past error terms in q
MA(q)
In
MA
(q)
linear
of average
past
error
terms
in in
q (2)
period
YtMA
period
t (q)
model,
at
 1aYtt- 1Y1value
 a(q)
t -...
is...
linear
at-function
Y
at
atMA
- 22model
athe

In
model,
value
is
average
past
error
terms
q period
tis
q
qq afunction
tY
- 1 2
2the
tas
- qfunction
backwards.
shown
follows:of of
In MA (q)
model,
is
the
linear
average
past
error
terms
in
q(2)
perio
t value
backwards.
MA
(q
)
model
is
shown
as
follows:
backwards.
MA
(q
)
model
is
shown
as
follows:
(2)
backwards.
MAYt(qvalue
) model is
asfunction
follows:of average past error terms in q period
In MA
model,
theshown
linear
Y(q)
t 
a1 at1-aa1 t- 1 is
...
(2)(2)
  at
a at
2 at2-a2ta
a
......q atq-aqt - aq
t Y
 q (2)
2
a
a
a
1 ,21,,…
t
q
Y

at


a
a
2 , ,…
t -1
2 ,……,
t - qthe error
backwards.
MA
(qt ,) model
follows:
t , , t -1t -1,is
t
tshown
-t1-2 ,……,
2 as
t - 2is
t terms,
-q
In the
above
model,
is theq error
terms,
,is qthe
is coefficients
the coefficients (
In
the above
model,
 q error
Yterms
  and
 at
 1average
at - 1 average
  2of
at - 2the
 ...
  q at - q
(2)
isthe
series.
terms
t and
error
… , of
isofthe
coefficients
at -qaseries.
 q q
aist athe
at t -1at -1at -2at -2 of the




1
2
t
q
, ,at, a,t -1 ,……,
isa the
error
terms,
,1 ,…
, , isthe
coefficients
In In
thethe
above
model,
2
at -2
error
terms,
coefficients
above
model,
- q the
q the
2, …
is the
error
terms,
the
above
,
, ,……,
,……, tis
is
the
error
terms, ,1 ,,…
, isis
is the
coefficien
In In
the
above
model,
model

ARMA
(p,q)
Model
is
the
average
of
the
series.
of
error
terms
and
ARMA
(p,q)
Model
a

is
the
average
of
the
series.
of of
error
terms
and
a
a
a



t
q
q
the
coefficients
of
error
terms
and
m
is
the
average
of
the
series.
series.
error terms
,……, of the
is the
error terms, 1 , 2 , … , is the coefficients
In the above
model,andt , t -1is, thet -2average

ismost
the
average
of
thepreocess
series.
of error
terms
andthe
ARMA
model,
the
most
stochastic
preocess
models,
is the
linear
function
of past
ARMA
(p,q)
Model
model,
stochastic
models,
is the
linear
function
of past
ARMA
(p,q)
Model
ARMA
(p,q)
Model
observations
and
error
terms.
ARMA
(p,q)
model
is
generally
shown
as
follows:
observations
and
ARMA
(p,q)error
Modelterms. ARMA (p,q) model is generally shown as follows:
linear function
of
past
ARMA
(p,q)
Model
ARMA
model,
the
most
preocess
thethe
function of(3)
past
Y

Φ
Y

Φ
YΦ
...
Φstochastic
- atδ -at
θ 1
atθ-models,
θ atθ- 22is
θ qlinear
atθ-linear
Y

Φ
Y
stochastic
...

amodels,
at -...
...
the
ARMA
model,
is
t
t  22 Y
p YΦ
t  p Yt δ
11 
qq a t - q
n as follows: ARMA
t 1 t 1model,
1 t 1 2the
2 most
p  preocess
t -12models,
2 is
thetmost
stochastic
preocess
linearfunction
functionof (3)
ofpast
pa
observations
and
error
terms.
ARMA
(p,q)
model
is
generally
shown
as
follows:
ARMA(3)
model,
the most
stochastic
preocess
models,is isgenerally
the linearshown
function
past
observations
andand
error
terms.
ARMA
(p,q)
model
asofas
follows:
 θ q at -q ARMA
observations
error
terms.
ARMA
(p,q)
model
is
generally
shown
follows:
the
most
the as
linear
of past
(3)(3)
Yt model,
Yt1Y

ΦY2error
Yt2Y2 tterms.
2Ystochastic
...
...
Φ
YtpYpt preocess
(p,q)
δ -δat
 θmodels,
aθt1generally
θ aist2-shown
θfollows:
aθtq-qafunction
observations
ARMA
model
Yt Φ
1Φ
Y
Φ

...pΦ
-δat
a2θt- 2a...
 ...
1 tand
1is
-1a t
qΦ
1Y
1Y
Y
p 
-1a2 θ
tΦ
- qa Φ p Φ p
Y
Y
Φ
Y

Φ

Φ


Φ
Y

at

θ

...

θ
t

p
Φ
t

t

2
t

p
observations
and
error
terms.
ARMA
(p,q)
model
is
generally
shown
as
follows:
1
2
t

1
t

2
t
1 ,t 1 , ,...,
2 ,...,
t  2 is the
ppast
t  p past
1 t -1values,
2 t -2
q 2t ,...,
-q
observation
, 1 ,,...,
is the
In third
equation,
is the
observation
values,
is the (
In third
equation,
Φ pYt  Φ1Yt 1  Φ2Yt  2  ...  Φ p Yt  p  δ - at  θ1 at -1 a θa2aat - 2a 
(3)
a ... at -θ2 q at -aq t -q(3)
at -the
1 , Φ2 ,...,
t , t -1
δ is δthe
q Φ error
es, Φcoefficient
thepast
t ,, t -1t -,2 ,……,
Y
constant,
is
forisfor
past
observation
values,
Yt Y1 ,t Y1t Y2 t,...,
is
the
constant,
,……,
is
the
error
coefficient
observation
values,
Φ
Φ
Y
Φ
t

p
p
Φ
Φ
1
2
t

p
p
is
observation
values,
, 1 the
is
InaInthird
equation,
2 ,...,
Y is
Φ pisthethe
Y Y2 t,...,
thepast
past
, ,...,
third
equation,
pthe
2 Y
1 ,Φ
2 ,...,
at -2
istthe
past
observation
values,F1,values,
F2values,
,...,Fp is Φ
third
equation,
,...,
is
the
pastobservation
observation
is th
third
equation,
 q  q Yt-1,,t Y1t-2,, ...,
t - q InIn

t-p


,……,
is
the
error
1
2
1
2
,
,
…
,
is
the
coefficients
of
error
terms.
terms
and
at -qat -Φ
, past
, for
… past
,observation
isYthe
coefficients
of
error
terms.a , aat ,aaat t……,a
terms and
Yvalues,
Yt 1observation
-1a,t -1at -2a,……,
δ
Φ
Φ
t values,
p
p
qathe
is
the
ercoefficient
is
the
constant,
t

2
t
2
δ
1
2
is
the
constant,
is
error
coefficient
for
a
a
a
, observation
,..., values,
isvalues,
the is
past
observation
values,
,..., is
the
Incoefficient
third
equation,
thethe
constant,
, t , ,t -1t-q, ,……,
error
forfor
past
observation
t
t-1, t-2
t - q the
t -,2 ,……,
δ is
constant,
isis the
err
coefficient
past
ror 
terms
and q1, qq2, … ,qq is the coefficients of error terms. a a

a
a


1
2
q
t
q
t
t
-1
t
2
δ
ARIMA
(p,d,q)
Model
, 1 ,,past
…
coefficients
of
error
terms.
terms
andand
2 , observation
ARIMA
(p,d,q)
Model
, is, the
isq the
coefficients
error
terms.
terms
isof
the
constant,
,
,……,
is the error
coefficient
for
values,
1 ,,…
2, …
is the
coefficients
of
error
terms. ,
terms
and
1 , 2 , … ,  q is the coefficients of error terms.
terms
and
To ARIMA
make
a non-stationary
timetime
series
stationary,
one one
or two
times
the the
difference-making
(p,d,q)
Model
To
make
a (p,d,q)
non-stationary
series
stationary,
or two
times
difference-making
ARIMA
Model
ARIMA (p,d,q)
Model
process
is
carried
out
and
the
result
are
shown
with
d.
The
model
that
is
applied
to the
process
is
carried
out
and
the
result
are
shown
with
d.
The
model
that
is
applied
to series
the series
es the difference-making
ARIMA
(p,d,q)
Model
To
make
a
non-stationary
time
series
stationary,
one
or
two
times
the
difference-making
94make
Journal
of or
Economic
and
Socialthe
Studies
Toto
make
a non-stationary
time
series
stationary,
oneone
twotwo
times
difference-making
hat is applied
the
series
To
a non-stationary
time
series
stationary,
or
times
the
difference-makin
process
is carried
outout
andand
thethe
result
areare
shown
with
d. d.
The
model
that
is applied
to to
thethe
series
process
is
carried
result
shown
with
The
model
that
is
applied
series
process
is carried out and
theseries
resultstationary,
are shown one
with or
d. two
The model
that difference-making
is applied
to the
seri
To make
a non-stationary
time
times the
process is carried out and the result are shown with d. The model that is applied to the series
ARIMA (p,d,q) Model
To make a non-stationary time series stationary, one or two times the differencemaking process is carried out and the result are shown with d. The model that is
applied to the series stationary by differencing is called as non-stationary linear stochastic model or integrated model shortly (Bircan & Karagöz, 2003).
Figure 1. Box-Jenkins Procedure
Box-Jenkins process operates as follows: (Dobre & Alexandru, 2008: 157).
Plot
Series
Is it Stationary?
Static?
Identify
Possible
Model
Difference
“Integrate” Series
Seriler
Diagnostic OK?
Make
Forecast
Adaptive Neuro-Fuzzy Inference System (ANFIS)
Fuzzy Inference System (FIS) consists of three conceptual components: fuzzy rule
base, data base and inference. In this system, the fuzzy rules and membership functions of input and output variables are determined by the user. The most important
step is to set the membership degrees of input and output variables. FIS techniques
aim at providing of significant inferences by using the linguistic rules (Ross, 2004).
Fuzzy systems do not have the skill to learn things, so they heavily depend on expert
opinion. Adaptive Neuro-Fuzzy Inference System (ANFIS), a hybrid model, was
first developed by Jang in 1993 in order to overcome this problem. This system
has combined the learning skill by artificial neural networks with inference skill of
expert opinion based FIS models (Jang, 1993). It adjusts the membership functions
of input and output variables and generates the rules related to input and output,
automatically. ANFIS can produce all the rules by using the dataset and enables
the researchers to interpret these rules. Therefore, it is the widely used model in the
studies of classification and estimation.
Volume 1
Number 2
July 2011
95
Adaptive Neuro-Fuzzy Inference System (ANFIS), a hybrid model, was first developed by
Jang in 1993 in order to overcome this problem. This system has combined the learning skill
by artificial neural networks with inference skill of expert opinion based FIS models (Jang,
1993). It adjusts the membership functions of input and output variables and generates the
rules related
to input
and output,
automatically.
can produce all the rules by using the
Rüstü YAYAR
& Mahmut
HEKIM &
Veysel YILMAZ & ANFIS
Fehim BAKIRCI
dataset and enables the researchers to interpret these rules. Therefore, it is the widely used
model in the studies of classification and estimation.
In an ANFIS
modelmodel
consisting
of two
output,the
thesetset
rules
In an ANFIS
consisting
of twoinputs
inputsand
and one
one output,
of of
rules
is as is as follows
(Jang, 1993):
follows (Jang, 1993):
Rule 1 : If x is A1 and y is B1 , then f1  p1 x  q1 y  r1
Rule 2 : If x is A2 and y is B 2 , then f 2  p 2 x  q 2 y  r2
where xxand
the the
inputs,
Ai andABand
are the
fuzzythe
sets,
fi are sets,
the outputs
the within the
Bi are
fuzzy
fi are within
the outputs
where
andy are
y are
inputs,
i i
,
q
and
r
are
the
design
fuzzy
region
specified
by
the
fuzzy
rule,
and
parameters
p
fuzzy region specified by the fuzzy rule, and parameters pi,i qii and rii are the design parameters
thatduring
are determined
duringprocess.
the training
Thearchitecture
ANFIS architecture
that areparameters
determined
the training
Theprocess.
ANFIS
to implement these
to
implement
these
two
rules
is
shown
in
Figure
2,
in
which
a
circle
indicates
a whereas
fixed
two rules is shown
in
Figure
2,
in
which
a
circle
indicates
a
fixed
node,
a square
Figure 2.
2. Structure
Structure of
of an
an ANFIS.
ANFIS.
Figure
Figure
2.
Structure
of
an
ANFIS.
node,
whereas
a
square
indicates
an
adaptive
node
(Jang,
1993).
indicates an adaptive node (Jang, 1993).
Figure 2. Structure of an ANFIS.
In the first layer, each node produces membership grades to which they belong to each
In
the first
layer,
each
node produces
membership
grades
to
which
they belong
to each
of the
In
layer,
each
produces
membership
grades
totooutputs
which
Inthe
thefirst
first
layer,
eachnode
nodesets
produces
membership
grades
whichthey
they
belong
toeach
eachof
ofthe
the
of the
appropriate
fuzzy
using membership
functions.
The
of
thisbelong
layer areto
appropriate
fuzzy
sets
using
membership
functions.
The
outputs
of
this
layer
are
the
fuzzy
appropriate
fuzzy
sets
using
membership
functions.
The
outputs
of
this
layer
are
the
fuzzy
appropriate
fuzzy
sets using
membership
Thebyoutputs of this layer are the fuzzy
the fuzzy
membership
grade
of the inputs,functions.
which are given
membership
grade
of
the
inputs,
which
are
given
by
membership
grade
of
the
inputs,
which
are
given
by
membership
grade
of
the
inputs,
which
are
given
by
1
O
(4)
(4)
OOii1i1 

A
AAii i(((xxx)))
(4)
(4)
1
11  B
(
)
O
y
(5)
(5)
OOii i BBii i 222((yy))
(5)
(5)
(small, large,
etc.)
areare
the the linguistic
Where,
and the
y arecrisp
the crisp
inputs
ith
node,
Ai andBBi (small,
xx and
yx are
inputs
to
iito
th
node,
A
large,
etc.)
Where,
crisp
toto
th
AAii iand
and
large,
etc.)
Where,
xand
andyyare
arethe
the
crispinputs
inputs
ithnode,
node,membership
andBBii i(small,
(small,
large,
etc.)are
are, the
thelinguistic
linguistic
Where,linguistic
and
mB
labels
characterized
by
appropriate
functions
mA
i
i

A
and

B
,
respectively.
labels
characterized
by
appropriate
membership
functions
i and
i , ,respectively.

A

B
labels
by
appropriate
membership
functions

A
and

B
respectively.
labelscharacterized
characterized
by
appropriate
membership
functions
ii
ii
respectively.
In the
the second
layer,layer,
every
node
incomingsignals
signals
sends
the product
product out.
In the second
every
nodemultiplies
multiplies the incoming
and and
sendssends
the prodIn
In the second
second layer,
layer, every
every node
node multiplies
multiplies the
the incoming
incoming signals
signals and
and sends the
the product out.
out.
Each
node
output
represents
the
firing
strength
of
a
rule.
uct
out.
Each
node
output
represents
the
firing
strength
of
a
rule.
Each
node
output
represents
the
firing
strength
of
a
rule.
Each node
output represents the firing strength of a rule.
2
O
(6)
OOii2i2 
w
wwii i 

AAAii (((xxx)))

BBBii (((yyy)))
(6)
(6)
(6)
i
i
In
the third
layer, the
main objective
is to calculate the
ratio of
each iith
rule’s firing
strength
In
Inthe
thethird
thirdlayer,
layer,the
themain
mainobjective
objectiveisistotocalculate
calculatethe
theratio
ratioof
ofeach
each th
ithrule’s
rule’sfiring
firingstrength
strength
wi is
is taken
taken as
as the
the normalized
normalized firing
firing
to the
the sum
sum of
of all
all rules’
rules’ firing
firing strength.
strength. Consequently,
Consequently, w
to
wi is taken as the normalized firing
to the 96
sum of all rules’ firing strength. Consequently,
Journal of iEconomic and Social Studies
strength
strength
strength
w
Oi333 
(7)
 w  wwii i
O
(7)
Oi i wwii i  w1  w
(7)
ww11ww222
In the third layer, the main objective is to calculate the ratio of each ith rule’s firing
strength to the sum of all rules’ firing strength. Consequently, wi is taken as the
normalized firing strength
Oi3 = wi =
wi
w1 + w2
(7)
In the fourth layer, the nodes are adaptive nodes. The output of each node in this
layer is simply the product of the normalized firing strength and a first order polynomial (for a first order Sugeno model). Thus, the outputs of this layer are given by
Oi4 = wi f i = wi ( pi x + qi y + ri )
(8)
where wi is the ith node’s output from the previous layer. Parameters pi, qi and ri
are the coefficients of this linear combination and are also the parameter set in the
consequent part of the Sugeno fuzzy model.
In the fifth layer, there is only one single fixed node. This single node computes the
overall output by summing all the incoming signals as follows
f =
∑w
i
i
fi
∑w (p x + q
=
∑w
i
i
i
i
i
y + ri )
(9)
i
Accordingly, the defuzzification process transforms each rule’s fuzzy results into a
crisp output in this layer.
In this study, the ANFIS was trained by hybrid learning algorithm which is highly
efficient in training the ANFIS. This learning algorithm adjusts all parameters {ai, bi,
ci} and {pi, qi, ri} to construct the ANFIS output match the training data. When the
premise parameters ai, bi and ci of the membership functions are fixed, the output of
the ANFIS becomes as follows:
f = w1 f1 + w2 f 2
= w1 ( p1 x + q1 y + r1 ) + w2 ( p 2 x + q 2 y + r2 )
(10)
Where, p1 , q1 , r1 , p 2 , q 2 and r2 are the adjustable resulting parameters? The least
squares method is widely used to easily identify the optimal values of these parameters (Jang, 1993).
Volume 1
Number 2
July 2011
97
ARIMA and ANFIS Applications
We benefited from autocorrelation and partial autocorrelation functions of the related series in order to obtain ARIMA models. The appropriate models for applications
were investigated based on the monthly electric data between years 2002–2010.
After choosing the models, the monthly electric values pertaining to the period between the first half of 2010 and second half of 2011 were estimated by the models.
Then, the forecasting values relating to the second half of 2010 were compared with
the real values of the same period.
Seven different models based on the subscriber groups were tested for the investigations. They are total electric use (Model 1), electric use in private houses (Model
2), electric use in industrial organizations (Model 3), electric use in business firms
(Model 4), electric use in government agencies (Model 5), electric use in other subscriptions (Model 6), and electric use in business firms-government agencies-other
subscriptions (Model 7). In the implemented experiments, we observed that there is
no ARIMA model appropriate for Model 1 and 7.
Experiment 1.
Analysis of total energy use (Model 1)
In the construction stage of an appropriate ARIMA model related to the consumption of total energy use, we determined that the change of energy consumption versus months is non-stationary. The difference of the monthly energy series was taken
once in accordance with the autocorrelation and partial autocorrelation function
graphs. When the difference was once taken, the series had got stationray character
in model validation stage. However, the ARIMA techniques generated through tests
are to pass the suitability test in order to be used for future forecastings. Thus, it is
indicated that the autocorrelation coefficients of the forecastings generated through
the ARIMA techniques show a trend of systematicity in the suitability test. Despite
all those efforts put forward, no model was detected as appropriate for this purpose.
When the ANFIS model was trained by the training dataset for 1000 iterations,
it found three rules for this experiment. The results obtained by ANFIS model are
shown in Figure 3, where the test result of the model is red line and the forecasting
of the next six month period is green line as follows:
98
Figure 3. The ANFIS output for Model 1.
As seen in Figure 3, there is a small decrease possibility, but the stationary case will
be lasting in the next six months. The comparative results of ARIMA and ANFIS
techniques are given in Table 1:
Table 1. Forecasting of total electric use (Model 1)
Month
Jul.10
Real
ARIMA
Forecasting
ANFIS
MSE
Forecasting
42,0229
50,9282
ug.10
51,4488
50,9275
ep.10
59,9116
50,9268
ct.10
43,4847
50,9261
ov.10
46,3052
50,9254
Dec.10
48,5912
Jan.11
o appropriate model has
been found
50,9240
50,9233
Mar.11
50,9226
pr.11
50,9219
May.11
50,9212
Jun.11
50,9205
Number 2
July 2011
40,4117
50,9247
eb.11
Volume 1
MSE
99
As seen in Table 1, the ARIMA could not achieve any forecasting result. However,
when the ANFIS was tested by six-month testing dataset, its mean square error
(MSE) ratio was 40.4117. The forecasting obtained by the ANFIS for the next six
months was close to the obtained test results of the ANFIS, so it can be observed
that there was approximately a stationary case.
Experiment 2.
Analysis of the electric use in private houses (Model 2)
In the construction stage of an appropriate ARIMA model related to the consumption of electric energy use in private houses, we determined that the change of energy consumption versus months is non-stationary. The difference of the energy series is once taken in accordance with the autocorrelation and partial autocorrelation
function graphs. When the difference taken, the series showed stationary haracter
in the model validation stage. As a result of the tests, ARIMA(1,1,2) was chosen as
the model.
it found eight rules for this experiment. The results obtained by ANFIS model are
100
As seen in Figure 4, there is a constant increase in the next six months in Model
2. The comparative results of ARIMA (1,1,2) and ANFIS techniques and the real
values for the period between 2002-2010 are given in Table 2:
Table 2. Forecasting of the electric use in private houses (Model 2)
ARIMA(1,1,2)
ANFIS
Month
Real
Jul.10
18,9146
21,1999
22,0048
ug.10
22,9082
21,3377
22,4716
ep.10
32,8206
21,4178
ct.10
19,9593
21,5264
ov.10
20,9913
21,6209
23,8837
Dec.10
23,7073
21,7224
24,3547
Jan.11
21,8205
24,8256
eb.11
21,9202
25,2962
Mar.11
22,0191
25,7668
pr.11
22,1184
26,2372
May.11
22,2175
26,7077
Jun.11
22,3167
27,1781
Forecasting
MSE
24,0842
Forecasting
22,9416
23,4125
MSE
21,3410
As seen in Table 2, the MSE ratio was 24.0842 for ARIMA (1,1,2) and 21.3410 for
ANFIS in the result of forecasting implemented by the six-month testing data for
Model 2. Thus, it can be said that the ANFIS provided a more successful forecasting
than the ARIMA.
Experiment 3.
Analysis of the electric use in industry (Model 3)
We experienced that the monthly energy change is originally unsuitable for the
validation of a model in the set stage of an appropriate ARIMA model to be applied in electric use in industry. After the analysis on the autocorrelation and partial
autocorrelation function graphs of the series employed in industrial electric use, the
difference was taken twice. Then, the series was made suitable for the analysis. After
a few testing, the model was selected as ARIMA (1,2,1).
Volume 1
Number 2
July 2011
101
it found two rules for this experiment. The results obtained by ANFIS model are
Figure 5. The ANFIS output for Model
As seen in Figure 5, the next six months is constantly stationary for Model 3. The
comparative results of the real values in the period between 2002-2010 and ARIMA
(1,2,1) and ANFIS techniques are given in Table 3.
Table 3: Forecasting of the electric use in the industry (Model 3)
ARIMA(1,2,1)
Months
Jul.10
Real
Forecasting
ANFIS
MSE
Forecasting
6,5457
11,1835
6,4739
ug.10
6,6035
8,3942
6,1838
ep.10
6,7541
9,1898
ct.10
7,0919
8,2417
ov.10
6,7017
8,1281
6,1088
Dec.10
5,9649
7,6015
6,0901
Jan.11
7,2656
6,0714
eb.11
6,8283
6,0527
Mar.11
6,4308
6,0340
pr.11
6,0049
6,0153
May.11
5,5836
5,9967
Jun.11
5,1508
5,9780
102
6,1138
6,1471
6,1275
MSE
0,3079
As seen in Table 3, the MSE ratio is 6.1138 for ARIMA (1,1,2) and 0.0379 for
ANFIS in the result of forecasting made through the six-month testing data for
Model 3. Thus, it can be said that ANFIS provided a more successful forecasting
than the ARIMA.
Experiment 4.
Analysis of the electric use in business firms (Model 4)
While a model related to the electric use in business firms was constructed, monthly
energy change was analyzed. But, it was determined that the series was originally unsuitable to construct an appropriate model. After the analysis on the autocorrelation
and partial autocorrelation function graphs, the series was observed to be appropriate
for an analysis stage when the difference was once taken. After a few testing, ARIMA(1,1,1) was determined to be the most appropriate model for this experiment.
it found four rules for this experiment. The results obtained by ANFIS model are
As seen in Figure 6, there was very quickly rise in the next six months for Model
4. The comparative results of the real values in the period between 2002-2010 and
ARIMA(1,1,1) and ANFIS techniques are given in Table 4.
Volume 1
Number 2
July 2011
103
Table 4: Forecasting of electric use in business firms (Model 4)
Months
Jul.10
Real
ARIMA(1,1,1)
Forecasting
ANFIS
MSE
Forecasting
5,1655
6,6010
6,9789
ug.10
9,5100
7,1028
7,1073
ep.10
9,4926
7,0126
ct.10
5,8424
7,1121
ov.10
6,5950
7,1508
7,5016
Dec.10
7,4564
7,2089
7,6370
Jan.11
7,2608
7,7745
eb.11
7,3147
7,9142
Mar.11
7,3680
8,0561
pr.11
7,4215
8,2001
May.11
7,4749
8,3462
Jun.11
7,5283
8,4943
2,6646
7,2370
7,3683
MSE
2,8888
As seen in Table 4, the MSE ratio is 2.6646 for ARIMA (1,1,1) and 2.888 for
ANFIS as a result of the forecasting through the six month testing data for Model 4.
Thus, it can be said that ARIMA is little more successful in the implemented experiment when compared to ANFIS.
Experiment 5.
Analysis of the monthly electric use in government agencies (Model 5)
While constructing a model for the electric use in government agencies, the graphs
of monthly energy change were used in hand as a basis. It was determined that the
series was originally unsuitable for model validation. After the analysis on the autocorrelation and partial autocorrelation function graphs, the series was, then, found
to be suitable for an analysis stage when the difference was once taken. After a few
testing, the model was selected as ARIMA (2,1,1).
it found four rules for this experiment. The results obtained by ANFIS model are
104
As seen in Figure 7, there is a constant decrease in the next six months for Model
5. The comparative results of ARIMA (2,1,1) and ANFIS techniques and the real
values in the period between 2002-2010 are given in Table 5.
Table 5: Forecasting of the electric use in government agencies (Model 5)
ARIMA(2,1,1)
Month
Jul.10
Real
Forecasting
MSE
ANFIS
Forecasting
4,2125
3,3762
3,5093
ug.10
3,9930
3,6692
3,5053
ep.10
2,6223
3,4032
ct.10
3,0580
3,4401
ov.10
3,6314
3,3647
3,4604
Dec.10
4,2085
3,3635
3,4337
Jan.11
3,3431
3,4011
eb.11
3,3429
3,3627
Mar.11
3,3415
3,3184
pr.11
3,3467
3,2686
May.11
3,3531
3,2131
Jun.11
3,3620
3,1522
Volume 1
Number 2
July 2011
0,3909
MSE
0,3841
3,4961
3,4812
105
As seen in Table 5, the MSE ratio is 0.3909 for ARIMA(2,1,1) and 0.3841 for
ANFIS in the result of the forecasting made through the six month testing data for
Model 5. Thus, it can be said that ANFIS is little more successful in the forecasting
when compared to ARIMA.
Experiment 6.
Analysis of electric consumption of the others (Model 6)
Model testing named the others about the electric consumption of the subscriber
groups for six months was done. It was determined that the series was not appropriate to construct a model in its original. Thus, the series became appropriate after the
difference was once taken through the autocorrelation and partial autocorrelation
function graphs. After several tests, the model were determined as ARIMA (1,1,1).
As seen in Figure 8, there will be a little increase in the next six months for Model 6. In
Table 6, there are comparative results of the real values from the period of 2002-2010
and the techniques of ARIMA (1,1,1) and ANFIS in Model 6.
106
Table 6: Electric Consumption Forecasting of the Others (Model 6)
Months
ARIMA(1,1,1)
Real
Forecasting
MSE
ANFIS
Forecasting
em.10
7,1845
8,1967
7,4670
Ağu.10
8,4338
8,2828
7,5274
yl.10
8,2217
8,3353
ki.10
7,5329
8,3873
as.10
8,3855
8,4392
7,7085
ra.10
7,2539
8,4912
7,7689
ca.11
8,5431
7,8293
Şub.11
8,5951
7,8897
Mar.11
8,6470
7,9501
is.11
8,6990
8,0104
May.11
8,7509
8,0708
Haz.11
8,8029
8,1312
0,5540
7,5877
7,6481
MSE
0,3401
As seen in Table 6, MSE ratio is 0.3401 for ANFIS whereas it is 0.5540 for ARIMA
(1,1,1) as a result of the forecasting which was done by using test data for six months
for Model 6. Thus, ANFIS provided a more successful forecasting than ARIMA for
Model 6.
Experiment 7.
The analysis of electric consumption of the Business firm, State office and others
(Model 7)
It was determined in the forecasting of modeling about the electric consumption
of the business firm, state office and others that consumed energy is non-stationary.
The series became stationary by taking the difference for once according to the autocorrelation and partial autocorrelation function graphs of the related series. The
ARIMA techniques which are obtained through several experiments must pass the
compliance test to be used as an forecasting model regarding the future. In the
compliance test which was done for this reason, it was determined that the autocor-
Volume 1
Number 2
July 2011
107
relation coefficients of the forecasting errors of the forecastings obtained through
the ARIMA techniques shows a systematic tendency. The appropriate model could
not be determined.
As seen in Figure 9, there will be a linear increase in the next six months for Model
7. In Table 7, there are the results of ANFIS model for Model 7.
108
Table 7: Electric Consumption Forecasting of the Commerce Houses,
State Offices and Others (Model 7)
Months
ARIMA
Real
Forecasting
ANFIS
MSE
Forecasting
em.10
16,562
17,5558
Ağu.10
21,937
17,6570
yl.10
20,336
17,7583
ki.10
16,433
17,8599
as.10
18,612
17,9616
ra.10
18,918
ca.11
o appropriate model has
been found
MSE
4,8571
18,0636
18,1660
Şub.11
18,2690
Mar.11
18,3730
is.11
18,4789
May.11
18,5878
Haz.11
18,7017
As seen in Table 7, there is not any forecasting through ARIMA for Model 7. MSE
ratio became 4.8571 as a result of the forecasting through ANFIS which was done by
using test data for six months. The estimated results of the next six months are similar
to the results obtained through ANFIS but there has been an increase at the least.
Conclusions
We implemented different seven experiments for estimating and analyzing electric
energy consumption in order to plan the production, transmission and distribution of electric energy and to determine the consequences of the events occurring
in the electric market. These experiments focus on the electric energy consumption
forecasting implemented by using ANFIS and ARIMA techniques including the
analyses of total energy consumption, household electric consumption, industrial
electric consumption, commerce house electric consumption, monthly electric con-
Volume 1
Number 2
July 2011
109
sumption in state offices, electric of the others and the electric consumption of the
commerce houses, state offices and the others. This is especially guiding key for the
investors planning the investments in the electric sector.
There has been a preparatory work for the necessary precautions regarding the
electric in Tokat, revealing the electric consumption structure of Tokat province.
The electric demand structure of Tokat regarding the previous consumption of
Tokat province and the estimated electric energy for the future has been revealed.
Although the study which was conducted through ANFIS and ARIMA techniques
in the field of electric energy consumption was conducted on regional basis, it can
be a pilot study for the extensive national and international studies on the energy
consumption.
Electric energy demands for the tested periods and the first six months of the year
2011 were estimated by using the ARIMA and the ANFIS techniques. Every forecasting experiment related to the electric consumption performed by ANFIS and
ARIMA showed that ANFIS is more successful estimator. The ARIMA was more
successful in only an forecasting experiment. In addition to this, an appropriate
ARIMA model could not have been found for two forecasting experiments. As a
result, the ANFIS is more appropriate than the ARIMA in the forecasting studies
regarding the electric consumption.
References
Al-Garni, A.Z. & Abdel-Aal R.E. (1997). Forecasting Monthly Electric Energy
Consumption in Eastern Saudi Arabia Using Univariate Time Series Analysis,
Energy, Volume 22, Issue 11, 1059–1069.
Al-Garni, A.Z. & Javeed Nizami, S. S. A. K. (1995). Forecasting Electric Energy
Consumption Using Neural Networks, Energy Policy, Volume 23, Issue 12,
1097–1104.
Asilkan, Ö. & Irmak, S. (2009). Forecasting the Future Prices of the Second Hand
Automobiles Through Neural Networks, Journal of Faculty of Economics And
Administrative Sciences, Volume: 14, 2, 378.
Bircan, H. & Karagöz, Y. (2003). A Practice on The Monthly Exchange Rate Forecasting
Through the Box-Jenkins Models, Journal of Social Sciences of Kocaeli University,
Issue:6/2, 49, 51.
110
Bozkurt, H. (2007). Analysis of Time Sequences, Ekin Publishing House, Bursa, 7–8.
Brown R.E. & Koomey J.G. (2002). Electricity Use in California: Past Trends and
Present Usage Patterns, Enduse Forecasting and Market Assessment, http://enduse.lbl.gov/info/LBNL-47992.pdf.
Çebi, H. & Kutay, F. (2004). Forecasting of The Turkey’s Electrical Energy Consumption
Until 2010 Through Artificial Neural Networks, J. Fac. Eng. Arch. Gazi Univ.,
Volume 19, No 3, 227-233, http://www.mmfdergi.gazi.edu.tr/2004_3/227234.pdf.
Demir, A. (1968). A Study on World’s Economy, SBF Publications of Ankara
University No.259 Ankara, 68.
Demirel, Ö. & Kakilli, A. & Tektaş, M. (2010). Forecasting of Electrical Energy
Load Through Anfis And Arima Models, Journal of Faculty of Engineering And
Architecture Volume J. Fac. Eng. Arch. Gazi Uni. 25, No:3, 602.
Dikmen, N. (2009). Basic Concepts and Applications of Econometrics, Nobel
Publication Distribution, Ankara.
Dobre, I. & Alexandru, A. A. (2008). Modelling Unemployment Rate Using BoxJenkins Procedure, Journal of Applied Quantitative Methods, 157.
Electricity Generation Corporation (2011). www.euas.gov.tr.
Governorship of Tokat (2006). Province Annual of 2006, Tokat, 39, 146.
Gujarati, D.N.(2009). Translators Şenesen, G. G. & Şenesen, Ü., Basic Econometrics,
Sixth Edition, Literature Publication, İstanbul, 378.
Jang, J. S. R., (1993). ANFIS: Adaptive-Network Based Fuzzy Inference Systems, IEEE
Transaction on Systems, Man, and Cybernetics, 23 (03): 665-685.
Kılıç, N. (2006). A General Overview On Turkey’s Electrical Energy Consumption And
Production, Izmir Chamber of Commerce, R&D Journal, July 2006, İzmir, 12.
Lise, W. & Van Montfort, K. (2005). Energy Consumption And Gdp in Turkey: is
There a Cointegration Relationship? June 29 – July 2, 2005, Istanbul, Turkey, 5.
Official Gazette, (2006). Regulations on Activity Report by Public Administrations,
17.03.2006, Issue: 26111.
Önder, E. & Hasgül, Ö. (2009). Use of Box-Jenkins Model on the Forecasting of
Foreign Visitors, Time Sequence Analysis Through the Winters Method And
Artificial Neural Networks Winters, Administration, Year: 20, Issue: 62, 62-83.
Provincial Department of Environment and Foresty of The Governorship of Tokat,
(2007). Environment Status Report of 2007 of Tokat, Tokat, 1, 130.
Ross, T. J. (2004). Fuzzy Logic with Engineering Applications, Second edition, John
Wiley.
Şekerci Öztura, H.(2007). Today and Tomorrow of Electrical Energy In Our
Country, VI. Energy Symposium of Union of Chambers of Turkish Engineers And
Architects - Global Energy Policies And The Reality of Turkey, Ankara, 268.
Tak S. (2002). Methods of Electrical Energy Demand Estimation and An Econometric
Practice for Turkey (1970–2005), Unpublished Postgraduate Thesis, Atatürk
University, Erzurum, 47.
Terzi, H. (1998). Relationship Between Electricity Consumption and Economic Growth
in Turkey : A Sectoral Comparision, Journal of Business and Finance, Volume:
13, Issue:144, March 1998, 62-71.
Tufan, E. & Hamarat, B. (2003). Clustering of Financial Ratios of the Quoted Companies
through Fuzzy Logic Method, Journal of Naval Science and Engineering, Vol. 1,
No:2, 123-140.
Turkish Statistical Institute (TUIK) (2011). http://report.tuik.gov.tr/reports/
rwservlet?ad
nksdb2=&ENVID=adnksdb2Env&report=ikametedilen_
il.RDF&p_kod=2&p_kil1=60&p_yil=2010&p_dil=1&desformat=html.
Turkish Statistical Institute (TUIK) (2009). Regional Indicators, 2009 TR 83 Samsun,
Tokat, Amasya, April 2010 Ankara, 10.
VIII. Regional Directorate of State Hydraulic Works - Samsun, (2011). http://
www2.dsi.gov .tr/bolge/dsi7/tokat.htm#atakoy.

com hekim tr

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