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DYNAMIC ECONOMETRIC MODELS 
Vol. 9 – Nicolaus Copernicus University – Toruń – 2009 

Aneta Włodarczyk, Marcin Zawada 
Politechnika Częstochowska 

The Use of Weather Variables in the Modeling  
of Demand for Electricity in One of the Regions  

in the Southern Poland  

A b s t r a c t. The main objective of the paper is the verification of usefulness of the ARFIMA-
FIGARCH class models in the description of tendencies in the energy consumption in a selected 
region of the southern Poland taking into consideration weather variables. 

K e y w o r d s: weather variables, the ARFIMA-FIGARCH class model, weather risks.  

1. Introduction 
 The companies specializing in the production or distribution of power are 
particularly exposed to the weather risk, understood as the possibility of change 
in the financial result of a company caused by the variability of daily weather 
conditions: air temperature, rainfall and snowfall, sun light exposure, wind 
speed and humidity. Furthermore, the inability to store the power leads to the 
necessity of a precise measurement of the future demand for electricity by the 
companies specialising in its sale. Therefore the search for statistical and eco-
nometrical tools enabling the modeling and forecasting of the demand for power 
in varying weather conditions has become such an important research problem.  

2. Review of Research in the Scope of the Impact of the Climatic 
Factors on the Electrical Energy Consumption  

 Identification and measurement of the weather risk are connected with the 
necessity to isolate from the observable electrical energy consumption a part 
which is sensitive to the effects of climatic factors. While analyzing historical 
time series relating to the demand for electrical energy, containing daily, weekly 
or monthly data from a dozen years, one may notice a strong long-term tenden-
cy, whose occurrence has been affected by social, demographic and economic 



Aneta Włodarczyk, Marcin Zawada 

 

 

100 

factors. In order to isolate the demand for electrical energy which is sensitive to 
weather factors, various ways of data filtration can be used. In empirical re-
search on modeling the above relation the following methods are used:  

1. the method of the decomposition of time series into the trend component,  
the calendar component, the periodic component and the irregular compo-
nent (Moral-Carcedo, Vicéns – Otero, 2005; Bessec, Fouquau, 2008):  

,
1

,0 ∑
=

++++=
m

j
tttaug

j
jt FEWDItE κδαα  (1) 

or 

,3
3

2
210 ttt FEYtttE +++++= δαααα   (2) 

where Et is the demand for electricity, Iaug,t is a dummy variable taking the 
value 1 if the observation of the demand corresponds to the month of Au-
gust, WDt is the variable describing working day effect, Yt is the seasonal 
unadjusted production in total manufacturing at time t, FEt is  the electricity 
demand with the deterministic component filtered out. 

2. the index-related equalization of the long term tendencies which do not re-
sult from weather conditions in terms of the demand for electrical energy 
(Sailor, Muñoz, 1997; Valor, Meneu, Casellles, 2001): 

,
j

ij
ij E

E
MSVI =  (3) 

,
jk

ijk
ijk E

E
DSVI =  (4) 

where MSVIij is the index value for month i in year j, Eij is the monthly 
electricity consumption for month i in year j, jE is the monthly average 
electricity load for year j, DSVIijk is the index value for day i of week j of 
year k, Eijk is the electricity consumption for this same day, jkE is the daily 
average electricity load for week j in year k. 

 After the estimation of the demand for electrical energy which is sensitive to 
climatic factors, the strength and nature of the relations between the weather 
variables and the electrical energy consumption should be assessed. Different 
types of models were used in the previous research: 

1. Pardo, Meneu, Valor (2002) estimated the following model: 

,

)()(

11

1

6

1
10

tt
k

ktk

i
itittt

HM

DCDDLHDDLtLE

εϖϕ

δγβαα

+⋅++

++++=

∑

∑

=

=  (5) 



The Use of Weather Variables in the Modeling of Demand for Electricity … 

 

 

101

,)1( 33
9

9
2

21 ttLLL ξεφφφ =−−−− K  (6) 

where Dit is dummy variable for daily data (D1t = 1 for Monday, D1t = 0 for 
other days of the week), Mit is dummy variable for monthly data (M1t = 1 
for January, M1t = 0 for other months of the year), Ht is dummy variable for 
holidays (Ht = 1 for holidays, Ht = 0 for other days of the year). 

2. Moral-Carcedo, Vicéns – Otero (2005) have constructed the following 
models in order to describe the non-linear relation between the energy con-
sumption and air temperature: 
a) switch regression model 

,tSttStt TMPFE εβμ ++=  (7) 

b) threshold regression model 
[ ] [ ]

( )
,

)Pr(

Pr
)Pr( 2

1
∑
=

==
==

St
ttt

ttt
tt

SSDFf

iSiSDFf
iS ψ  (8) 

⎪
⎩

⎪
⎨

⎧

>++
>=>++
<++

=
.2
,12
,1

3

2

1

ThTMPTMP
ThTMPThTMP
ThTMPTMP

DF

ttt

ttt

ttt

t

εημ
εγμ
εβμ

 (9) 

 In a warmer climate the relation between air temperature and energy con-
sumption has a non-linear character with the form resembling letter U (Valor, 
Meneu, Casellles, 2001; Sailor and Muñoz, 1997); i.e. the maximum demand 
for energy is observed at the low and high temperatures. The introduction of the 
HDD and CDD indices, which separate the winter and summer seasons, enables 
better quantification of the analysed relation. Furthermore, the research by other 
authors (Bessec and Fouquau, 2008; among others) proves that in the climate 
zone, which includes Poland, the effect of a bigger demand for energy in the 
summer season connected with the use of air conditioning equipment is not 
significant.  

3. Statistical Analysis of Characteristics of Analysed Time Series 
 For the purposes of this paper the authors used information concerning: 
power consumption (in kWh), air temperature (in oC) and wind speed (in m/s) in 
one of the regions in the southern Poland in the period from September 1, 2005 
to June 30, 2008. In the analysis and further calculations daily data was used in 
the following way:  
− the HDD index (heating degree days) was calculated on the basis of the re-

lation: HDD = max (0,180C – Ti),where Ti – average daily air temperature 
on day number i; 



 

 

102 

− the C
lation

 The f
weather v
cycles of 
grouping 

Figure 1. C
C
a

 In ord
consumpt
were dete
 One o
(with var
power. M
2009). W
this paper
(5, 10, 20
test statis
McLeod 

              
1 Table 

tion of the 
thors (Włod

DD index (c
n: CDD = ma
figure 1 pres
variables ind

f varying leng
of variances

Changes in th
CDD index, a
a region in the

der to analys
tion and par
ermined (cf. T
of the pheno
rious lengths

Meteorologica
While focusin

r the authors
0, 30, 40, 50)
stics were sig
and Li test 

                  
1 presents the 
tests used in th

darczyk, Zawad

Aneta Wło

cooling degr
ax (0,Ti - 180

ents the dail
dicating the 
gth) in the a
s. 

he daily powe
air temperatur
e southern Pol

se the charac
rticular weat
Table 1). 
omena chara
s of the cycl
al data have 

ng on the dem
s analysed th
) order with t
gnificant at t
are, in turn

                
results of the L

he paper, whose
da, 2006, p. 313

odarczyk, Marc

ee days) was
C). 
ly power con
existence o

average of an

er consumptio
re (middle pan
land from Sep

cteristics of
ther variable

acteristic for
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a similar ch

mand for pow
he significanc
the use of the
the 0.001 sig
n, the basis f

Ljung-Box test 
e results are sh

3-321).  

cin Zawada 

s calculated 

nsumption an
f similar tim

nalysed proce

on, the HDD i
nel) and wind

ptember 1, 200

the distribut
es, the basic

r the power 
weekly, annu
haracteristic 
wer and the 
ce of autocor
e Ljung-Box
gnificance le
for the conc

only for the or
hown in Table 

on the basis 

nd values of 
me structure 
esses and the

index (upper 
d speed (lowe
05 till June 30

tions of the 
c descriptive

market is p
al) in the de
(cf. Benth a
variables pr
rrelation to t

x test1. All the
vel. The resu

clusion that 

rder 30. A detai
1 was presente

 of the re-

f particular 
(for time 

e effect of 

 
panel), the 

er panel) in 
0, 2008 

electricity 
e statistics 

periodicity 
emand for 
and Benth, 
esented in 
the fiftieth 
e obtained 
ults of the 
there is a 

iled descrip-
d by the au-



 

 

strong co
ARCH ef

Table 1. D
St
M

Standar
Mi
Ma
Ske
Ku
L-
L-
K

Note: Symbo

 Air te
consumpt
nificantly

Figure 2. C
t
w

 The a
a signific
in the sha
cification
process o

The Use of Wea

orrelation of
ffect.  

Descriptive sta
tatistic 
Mean 
rd deviation 
nimum 

aximum 
ewness 
urtosis 
-B(30) 
B2(30) 

KPSS 
ol ** indicated the 

emperature a
tion, wherea

y lower (Figu

Correlative gr
tion, the HDD
wind speed an

analysis of c
ant stage of 
ape of analys
n of equation
of demand fo

ather Variables

f squares of 

atistics for the 
Consumption
4532400.0000
504420.0000
3204400.0000
5657800.0000

-0.2376 
-0.4689 

10188.3000**

10402.1000**

1.1764** 
significance of th

and the HDD
s the influen

ure 2).  

raphs presentin
D index and a
nd the CDD in

characteristic
econometric
sed variables
ns of conditio
or power. In 

s in the Modelin

f given serie

analysed vari
n Temperat
0 7.5579

0 8.4172
0 -20.208
0 26.0420

-0.3741
-0.3992

* 19372.20
* 16759.90

1.0654*

he result at the 0.

D index have
nce of wind f

ng the dispers
air temperatur
ndex (lower pa

cs of time se
c modelling, 
s brings effec
onal mean a
other words

ng of Demand f

es, which is 

iables 
ture W
9 3.4
2 1.5
80 0.4
0 11.9
1 0.9
2 1.3
00** 539.6
00** 498.9
** 0.87
01 level. Calcula

e the biggest
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eries made i
as the identi
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nd the condi
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for Electricity …

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495 1

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6100** 191
9290** 121
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ations made in G@

t impact on 
the CDD ind

for the energy
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n this part c
fication of re
rm of the rele
itional varian
the construct

… 103

ed by the 

HDD 
10.6700 
8.0799 
0.0000 
38.2080 
0.5307 
-0.3965 
103.6000** 
120.5000** 
1.0585** 
@RCHTM. 

the power 
dex is sig-

 
y consump-
nsumption, 

constitutes 
egularities 
evant spe-
nce of the 
tion of the 



Aneta Włodarczyk, Marcin Zawada 

 

 

104 

congruent econometric model according to the concept of Z. Zieliński 
(Zieliński, 1984).  

4. Estimation and Verification of Models of the Demand  
for Electricity  

 At the first stage of the research the authors identified a deterministic trend 
connected with the impact of demographic, economic and social factors on the 
demand for power in a region in the southern Poland. From the estimated vari-
ous models of trend for the daily power consumption the author selected a third 
degree polynomial trend, taking into account the value of determination coeffi-
cient and the significance of the estimates of structural parameters of the mod-
els.  Due to the object of the research, which was the description of the relation 
between the impact of weather factors on the energy consumption,  in the equa-
tion of demand for power the author included also the analysed weather va-
riables- giving them a dynamic structure. Additionally the equation includes 
also dummies, whose task is to describe a weekly periodocity, annual seasonali-
ty and holiday effect in the shaping of demand for energy. Finally the authors 
proposed the following specification of the model of energy consumption, ex-
pressed in logarithms:  

,

ln

6

1

11

1
13121

5

0

5

0
11

3
3

2
210

∑ ∑

∑ ∑

= =
+−

= =
−+−+

++++++

++++++=

i j
ttttjtjiti

k k
ktkktkt

uSSSMD

windtemptttE

κκκϕδ

βλαααα
 (10) 

where:  
Dit – dummy variable equals one for the day i, and zero otherwise,  
Mjt – dummy variable equals one for the month j , and zero otherwise,  
St  – dummy variable is equal to one for the holiday, and zero otherwise,  
St-1 – dummy variable equals one for the day preceding the holiday, and zero 

otherwise,  
St+1 – dummy variable is equal to one for the day following the holiday, and 

zero otherwise. 
 The models of power consumption without weather variables, including the 
impact of air temperature, wind,  as well as the HDD index were estimated with 
the OLS method. On the basis of information criteria, tests for model residuals 
and the parameter significance test the authors selected the following models 
with the weather variables (Table 2).  
 The results of parameter estimation of the model (10) indicate that the cur-
rent and one period lagged air temperature as well as one day lagged wind force 
have the significant impact on the power consumption in a given day. Moreo-



The Use of Weather Variables in the Modeling of Demand for Electricity … 

 

 

105

ver, estimates of parameters which stand by dummy variables and model peri-
odicity in the weekly cycle on demand on energy indicate that on Mondays, 
Saturdays and Sundays energy consumption is lower than the average level and 
higher in the other days of the week. In the case of dummy variables associated 
with monthly seasonal effects all estimates of parameters are significant and 
negative for summer months (May, June, July, August, and September). It is 
connected with the impact of seasonal factors, such as, air temperature, length 
of the day, level of sun light exposure on the demand for energy. All parameters 
standing by dummy variables associated with holidays and neighbouring days 
are statistically significant and negative which indicates that the energy con-
sumption on holidays and neighbouring days is significantly lower in compari-
son with regular working days (as indicated by results of the Wald test for 
equality of parameters). 

Table 2. Estimates of the parameters of the model (10) 
Parameter Coefficient p-value Parameter Coefficient p-value 

α0
 15.3739 0.0000*** φ1 0.0579 0.0000*** 

α1
 -0.0002 0.0000*** φ2 0.0261 0.0000*** 

α2
 4.336e-07 0.0000*** φ3 0.0262 0.0000*** 

α3
 -1.729e-010 0.0089*** φ4 0.0073 0.0667** 

λ1 -0.0009 0.0358** φ5 -0.0568 0.0000*** 
λ2 -0.0036 0.0000*** φ6 -0.0830 0.0000*** 
β2 0.0024 0.0040*** φ7 -0.0491 0.0000*** 
δ1 -0.0067 0.0235** φ8 -0.0478 0.0000*** 
δ2 0.0293 0.0000*** φ9 -0.0185 0.0000*** 
δ3 0.0392 0.0000*** φ10 0.0199 0.0000*** 
δ4 0.0408 0.0000*** φ11 0.0500 0.0000*** 
δ5 0.0404 0.0000*** κ1 -0.1845 0.0000*** 
δ6 -0.0059 0.0442* κ2 -0.0369 0.0000*** 

Adjusted R2 0.88326 κ3 -0.0859 0.0000*** 
AIC -3785.4470 - - - 
BIC -3652.0610 - - - 

Hannan-Quinn -3734.8310 - - - 
Note: The symbol *** indicates the significance of the result at the 0.001 level. Calculations made in Gretl. 

 In order to identify the autocorrelation effect, Box-Pierce test (the lag level: 
5, 10, 20, 50) has been used for residuals of model (10) – all test statistics indi-
cate for the significant autocorrelation in residuals. To verified the ARCH ef-
fect, two different test have been used: Engle test (for 1, 2, 5, 10, and 20 lags) 
for residuals and Box-Pierce test for squared residuals (level of lag: 5, 10, 20, 
50). Similarly, in this case all test statistics indicate for the significant autocor-
relation in squared residuals. Using the Geweke-Porter-Hudak test, the long 
memory effect in residuals and squared residuals of the electricity demand 



Aneta Włodarczyk, Marcin Zawada 

 

 

106 

model has been captured2. With regard to the verification of residuals proper-
ties, the model of ARFIMA (P, D, Q)-FIGARCH (p, d, q) class can be used for 
description of correlation between weather variables and energy consumption3:  

,)()()( ttt
D BuB εθμφ =−Δ  (11) 

),1,0(~z                , t IIDhz ttt ⋅=ε  (12) 

),)]((1[)( 2

1
,

2
tt

r

k
tkkt

d hBxB −−++=Δ ∑
=

εβωωεϕ  (13) 

where: jj

j

DD B
j

D
B )1()1(

0
−⎟⎟

⎠

⎞
⎜⎜
⎝

⎛
=−=Δ ∑

∞

=
 - filter difference of order D, 

ss

s

dd B
s
d

B )1()1(
0

−⎟⎟
⎠

⎞
⎜⎜
⎝

⎛
=−=Δ ∑

∞

=
 - filter difference of order d,  

-1< D < 0,5,  0 < d < 1,  0
1

, >+∑
=

r

k
tkk xωω , 

P
PBBB φφφ −−−= ...1)( 1 , Q

Q BBB θθθ +++= ...1)( 1 ,   
q

qBBB ϕϕϕ −−−= ...1)( 1 , p
pBBB βββ ++= ...)( 1 . 

 Introduction to the equation of conditional variance of regressor, which is 
a variability of weather factors or dummy variables which model periodicity of 
variance enables to connect dynamics of variability of energy consumption with 
variability of weather conditions of different structure of energy consumers in 
working days and holidays. In the current framework the following descriptive 
variables have been introduced to the equation of conditional variance of the 
process:4 dummy variables which model the effect of week day, dummy va-
riables which model the month effect in the year, dummy variables which mod-
el holidays, square of increment of daily average temperature in subsequent 
days, square of increment of wind power in subsequent days. 
 Orders of models ARFIMA(P,D,Q)-FIGARCH(p,d,q) were chosen on the 
basis of information criteria and significance of the model parameters. The best 
models in this class are presented in Table 3.  

                                                 
2 Because of limited size of this framework, results of conducted tests for model residuals 

have not been presented. 
3 In order to guarantee stationarity of analysed models of time series, it is assumed that roots 

of polynomial 0(B)  ,0)( == ϕφ B  lie outside the unit circle (Preś, 2007, p. 206; Laurent, 2007, 
p. 55–74). 

4 Because of large number of model parameters and problems associated with estimation, 
proposed variables were separately attached to the equation of conditional variance. 



 

 

Table 3. Parameter estimates of ARFIMA(1,1)-GARCH(1,1) models 
Parameter ARMA(1,1)-GARCH(1,1)+R ARFIMA(1,1)-GARCH(1,1)+R ARFIMA(1,1)-GARCH(1,1) 

Cst(M) 0.001950   [0.4575] 0.0020   [0.5154] 0.0023   [0.4644] 
D-ARFIMA - 0.0426   [0.6560] 0.04460   [0.6341] 

AR(1) 0.7198   [0.0000] 0.6904   [0.0000] 0.6774   [0.0000] 
MA(1) -0.0929   [0.0925] -0.1104   [0.0694] -0.0983   [0.1168] 
Cst(V) 0.0004   [0.0000] 0.0003   [0.0000] 0.0003   [0.0032] 

Dif(temp) 0.87e-5   [0.0000] 0.55e-5   [0.0000] - 
ARCH1 0.2611   [0.0000] 0.2091   [0.0000] 0.2314   [0.0049] 

GARCH1 0.2709   [0.0032] 0.4439   [0.0000] 0.3931   [0.0299] 
Skewness -0.1157   [0.0173] -0.1217   [0.0130] -0.1202   [0.0165] 
Df-Student 5.2049   [0.0000] 5.0735   [0.0000] 5.1046   [0.0000] 

AIC -4.3980 -4.3939 -4.3926 
SC -4.3549 -4.3460 -4.3494 
H-Q -4.3816 -4.3757 -4.3762 

Shibata -4.3981 -4.3941 -4.3927 
Note: p-values have been presented in the brackets. Calculations made in G@RCHTM. 

Table 4. Summary statistics for model residuals of models ARFIMA-GARCH 
Statistic ARMA(1,1)-

GARCH(1,1)+R 
ARFIMA(1,1)-

GARCH(1,1)+R 
ARFIMA(1,1)-
GARCH(1,1) 

Q (Box-Pierce) Statistics on Standardized Residuals 
Q(5) 4.76412   [0.1899] 4.9544   [0.1752] 4.7439   [0.1915] 
Q(10) 15.8704   [0.0443] 15.9747   [0.0427] 15.5973   [0.0485] 
Q(20) 29.4930   [0.0427] 30.0496   [0.0370] 30.0668   [0.0368] 
Q(50) 57.5181   [0.1633] 57.7321   [0.1586] 58.5882   [0.1407] 

Q (Box-Pierce) Statistics on Squared Standardized Residuals 
Q(5) 0.9382   [0.8162] 1.4152   [0.7020] 1.4080   [0.7037] 
Q(10) 3.9715   [0.8597] 4.8275   [0.7758] 5.0532   [0.7519] 
Q(20) 6.1725   [0.9954] 7.2110   [0.9882] 7.2413   [0.9879] 
Q(50) 27.6562   [0.9919] 27.9235   [0.9909] 27.3902   [0.9927] 

Engle’s LM  ARCH Test 
ARCH(1-2) 0.2695   [0.7638]    0.4347   [0.6476]    0.4418   [0.6430]    
ARCH(1-5) 0.1866   [0.9677]    0.2834   [0.9224]    0.2819   [0.9231]    
ARCH(1-10) 0.3822   [0.9547]    0.4635   [0.9137]    0.4853   [0.9003]    

Nyblom Stability Test  
Nyblom Statistic  

for parameter vector  
1.4860 
stability 

1.6558 
stability 

1.2591 
stability 

Nonstability parame-
ter by Nyblom test 

Nonstability  parameter    
MA(1) 

Nonstability parameter : 
D-ARFIMA,   AR(1),   

MA(1) 

Nonstability parame-
ters : 

D-ARFIMA,   MA(1) 
Sign Bias Test 

SB 1.6800   [0.0930] 1.7303   [0.0836] 1.7104   [0.0872] 
NSB 1.2895   [0.1972] 1.0867   [0.2772] 1.1378   [0.2552] 

The Joint Test 4.3732   [0.2239] 5.3313   [0.1491] 5.1391   [0.1619] 
Adjusted Pearson 

Goodness-of-fit Test 
Empirical distribution is 
congruent with theoreti-

cal distribution 

Empirical distribution is 
congruent with theoreti-

cal distribution 

Empirical distribution is 
congruent with theoret-

ical distribution 
Note: p-values have been presented in the brackets. Calculations made in G@RCHTM.  



Aneta Włodarczyk, Marcin Zawada 

 

108 

 When model estimates are assessed with regard to its quality the following 
results of tests conducted on its standardized residuals should be analysed: veri-
fication of uncorrelated standardized residuals (Box-Pierce test), lack of ARCH 
effect (Box-Pierce test for squared residuals and Engle’s test), testing parame-
ters stability in the model (Nyblom test), lack of diversity of influence made by 
negative and positive innovations on the level of variability (SB test),  lack of 
diversity of influence made by large and small negative (positive)  innovations 
on the variability (NSB test), fit of a distribution of empirical standardized resi-
duals with assumed distribution (Pearson’s chi-square goodness-of-fit test).5 
 Each time, the introduction of GARCH structure with conditional skewed 
distribution of t-Student has been made, the result was that the effect of group-
ing variances, which was present in residuals of ARFIMA model has been elim-
inated. In the case of different estimated models of ARFIMA-FIGARCH class 
the estimate of fractional integration parameter d in conditional variance equa-
tion was statistically insignificant. Even when dummy variables which model 
the effect of week day, month, and holidays in the equation of conditional va-
riance of the process were considered, the characteristics of the model were not 
improved significantly. Next, the authors introduce the variability of the weath-
er factors as the regressor to the  conditional variance equation of the electricity 
demand. The result is that the autocorelation effect, which is found in standar-
dized residuals of ARFIMA-GARCH model, has been decreased or eliminated.  

5. Summary 
 Demonopolization in energy industry in Poland has forced companies from 
energy industry to work out and implement internal procedures of risk man-
agement, because the risk is present in energy trade. Companies from this in-
dustry more and more often use weather derivatives to hedge against effects of 
weather risk, because this activity allows to make financial results independent 
of changing weather conditions. 
 Analysis of influence of particular weather factors on energy consumption 
conducted by the Authors concerned only a particular region of southern Pol-
and. Unfortunately, Polish conditions does not allow straight-forward access to 
these type of data because of the high cost of data purchase, whereas in many 
countries, databases concerning weather variables are available for free on web 
pages of meteorological stations of national entities which collect this type 
of data. 

Introduction to the equation of conditional variance of the regressor, which 
is a variability of average daily temperature increase in the coming days  
(Dif(temp)) enables to connect the dynamics of volatility of energy consump-

                                                 
5 All above-mentioned methods have been described in the econometric literature (Doman, 

Doman, 2004, p. 295–308; Laurent, 2007, p. 41–46).  



The Use of Weather Variables in the Modeling of Demand for Electricity … 

 

 

109

tion with the volatility of weather conditions. Moreover, the assessment of the 
ARFIMA-GARCH models on the basis of the residuals of model (10) made it 
possible to assess the conditional volatility of the process of demand for electri-
cal energy. With the use of conditional volatility one can measure the volatility 
of the demand for electrical energy, i.e. the risk related to unpredictable change 
in the energy consumption under the influence of e.g. changing weather condi-
tions. While extending analysis of the impact of weather factors on the function-
ing of the power energy industry branch company, one should apply the Value 
at Risk methodology to measure the weather risk. Such approach will make 
companies dealing with the energy production and sales aware of the potential 
losses they may suffer as a result of unexpected change of weather factors.  

References  
Benth, F. E., Benth, J. S. (2009), Dynamic Pricing of Wind Futures, Energy Economics, 31, 

16–24. 
Bessec, M.,  Fouquau, J. (2008), The Non-linear Between Electricity Consumption and Tempera-

ture in Europe: A Threshold Approach, Energy Economics, 30, 2705–2721. 
Doman, M., Doman, R. (2004), Ekonometryczne modelowanie dynamiki polskiego rynku finan-

sowego (Econometric modeling of the dynamics of the Polish financial market), Wydaw-
nictwo AE w Poznaniu, Poznań. 

Laurent, S. (2007), Estimating and Forecasting ARCH Models Using G@RCH™5, Timberlake 
Consultants Ltd, London. 

Moral-Carcedo, J., Vicéns – Otero, J. (2005), Modelling the Non-linear Response of Spanish 
Electricity Demand to Temperature Variations, Energy Economics, 27, 477–494. 

Pardo, A., Meneu, V., Valor, E. (2002), Temperature and Seasonality Influences on Spanish 
Electricity Load, Energy Economics, 24, 55–70. 

Preś, J. (2007), Zarządzanie ryzykiem pogodowym (Management of Weather Risk), Wydawnictwo 
CeDeWu, Warszawa. 

Sailor, D. J., Muñoz, J. R. (1997), Sensitivity of Electricity and Natural Gas Consumption to 
Climate in the U.S.A. – Methodology and Results for Eight States, Energy, 22, 987–998.  

Valor, E., Meneu, V., Casellles, V. (2001), Daily Air Temperature and Electricity Load in Spain, 
Journal of Applied Meteorology, 40,1413–1421. 

Włodarczyk, A., Zawada, M. (2006), Behavior of Prices in the Polish Power Exchange and Euro-
pean Power Exchanges. Statistical – Econometric Analysis, 3rd International Conference: 
The European Electricity Market EEM06. Challenge of the Unification, Warsaw, 313–321. 

Zieliński, Z. (1984), Zmienność w czasie strukturalnych parametrów modelu ekonometrycznego 
(Time Variability of Structural Parameters in Econometric Model), Przegląd Statystyczny 
(Statistical Survey), 1/2, 135–148. 

Zastosowaniem zmiennych pogodowych w modelowaniu zapotrzebowa-
nia na energię elektryczną w jednym z regionów Polski południowej 

Z a r y s  t r e ś c i. Głównym celem opracowania jest zweryfikowanie przydatności modeli klasy 
ARFIMA-FIGARCH do opisu kształtowania się zużycia energii elektrycznej w wybranym regio-
nie południowej Polski z uwzględnieniem zmiennych pogodowych.  

S ł o w a  k l u c z o w e: zmienne pogodowe, model ARFIMA-FIGARCH, ryzyko pogodowe. 



 

 

 


