Chapter 3
Load Forecasting Model
3.1 Introduction
Reviews of the load forecasting literature in the last chapter lead to the same
conclusion that the power tariff, GDP, and temperature are the key factors affecting
the load consumption. The relationship between load consumption and the key factors
may be specified by the general function
E t = f  Pt , GDPt , TEMPt 
t = 1, 2
T
(3.1)
where
E t = consumption of electricity energy in month t (gwh)
GDPt = gross domestic product in month (million baht)
TEMPt = temperature (celsius)
Pt = average power tariff in month t baht/kwh
Several monthly models of electricity energy consumption will be specified,
estimated, tested and selected as forecasting models for the electricity energy
consumption. Electricity energy consumption will be disaggregated and modeled for
the following categories
1) total consumption in the generating system
2) consumption in the northern generating system
3) consumption in the central generating system
4) consumption in the northeast generating system
5) consumption in the southern generating system
6) consumption in the PEA jurisdiction
7) consumption in the MEA jurisdiction
Data on electricity energy consumption, power tariff are monthly data
provided by the three power authorities. The temperature data are collected from the
Meteorological Department. The monthly power tariff is derived from the annual
revenue and sales of electricity energy of the relevant power authority by computing
the average monthly revenue per kWh. The monthly power tariff is thus constant for a
given year
Data on temperature are collected from the meteorological stations in each
region. Temperature days are computed for each station as the product of average
daily temperatures and the number of days in a given month. The average temperature
days for each region are then computed from the number of stations in that region.
Data on GDP are published only on an annual basis. Since the forecasting models are
monthly models, a proxy variable for monthly GDP is required. Since the
relationship between money supply and GDP is well established in macroeconomic
26
theory, and the data on money supply are available on a monthly basis, the money
supply is selected as a proxy variable for GDP in the monthly forecasting models.
Empirical test supports the money supply/GDP hypothesis when money
supply in the narrow sense,M1, can explain 97 percent of the total variations in GDP.
The general function of (3.1) may now be specified as
E t = f  Pt ,M1t ,TEMPt 
(3.2)
where M1t is the money supply in month t
3.2 Model Specification
The simple linear form of (3.2) is specified as
(3.3)
E t = A + A1M1t + A 2TEMPt + A3Pt
with A1 > 0 A 2 > 0 and A 3 < 0
The above model is fitted from the data between October 1991 and September
2003 with the following results
E t =  3933.97 + 0.011393 M1 + 7.05076 TEMPt + 62.4324 Pt
(t = –7.98) (t = 19.42)
(t = 13.20)
adj.R 2 = 0.9504
(t = 0.25)
(3.4)
Even though the simple linear model can explain 95 percent of the variations
in electricity energy consumption, the price variable has a “wrong’ sign. The wrong
sign of the price variable is the model’s shortcoming which needs to be addressed.
3.2.1
Distributed lag and Autoregressive Models
There may be some lags in the relationships between the exogenous variables
and the endogenous variable. Models with lagged variables may be specified by a
general function

E t = f Pt i , M1t  j , TEMPt k , E t h

i, j, k, h = 0, 1, 2
(3.5)
Lagged relationship between variables in the model may be explained by
diverse behaviors of the power consumers. As a case in point, the power tariff
structure in Thailand has a Ft mechanism for the adjustment of the tariff rate when
there are changes in the generation costs. The rate is adjusted every four months so a
power consumer has no knowledge of the tariff rate in month t since the rate he pays
in month t is actually the ‘average tariff rate’ of the last four months.
27
One possible hypothesis in this case is that electricity energy consumption of a
power consumer depends upon the anticipated tariff rate in month t. The model may
thus be specified as
E t = a + b*Pˆt + c*M1t + d*TEMPt
(3.6)
where E t = electricity energy consumption in month t
P̂t = anticipated power tariff in month t
and b < 0 c > 0 d > 0
There are no direct data on the anticipated tariff rate but it may be modeled by
a given behavioral assumption. As an example, the difference between anticipated
tariffs in month t and month t-1 depends on the anticipation error in month t–1 or

Pˆ t  Pˆ t 1 = e Pt 1  Pˆ t 1

(3.7)
where e > 0
Rewriting 3.7 in the form
P̂t 1  vB  = ePt 1
(3.8)
where
v = 1  e 
B = Backward operator
Substitution of (3.8) into (3.6) yields
Et = a +
b*e
Pt 1 + c*M1t + d*TEMPt
1  vB
(3.9)
Rearranging (3.9) leads to the expression
E t 1  vB = a 1  vB + b*ePt 1 + c 1  vB  M1t + d 1  vB  TEMPt
(3.10)
and the hence the autoregressive form
E t = J + b*ePt 1 + cM1t + c*vM1t 1 + d*TEMPt + d*vTEMPt 1 + vE t 1 (3.11)
where b*e < 0, c > 0, d > 0
28
The model specification in (3.11) is estimated for the case of Thailand. The
estimation results are not satisfactory since the price variable has a wrong sign. In
practice, the model specification of (3.5) is not known ex ante. The “correct”
specification is hidden behind the pattern of electricity consumption. It is proposed to
unveil the model specification by incorporating the Box–Jenkins (BJ) and the error–
correction (EC) techniques into the modeling process.
3.2.2
Concept of the Autoregressive Model
The error correction concept (EC) utilizes information from the model errors
to improve the model performance. The EC technique has been applied to several
studies such as the Sik and Frederick residential consumers’ demand for electricity
energy report.16 The BJ and EC techniques may be incorporated into the modeling
procedure in the two phases.
In the first phase, the model (3.2) is estimated by the simple OLS method in the
simple linear form
E t = A + A1Pt + A 2 M1t + A3TEMPt + z t
(3.12)
where z t = error term
The model errors are analyzed for their systematic pattern in the second phase
and used to improve the model performance. The error of (3.12) in month t is
specified by
z t = E t  Eˆ t = E t  A  A1Pt  A2 M1t  A3TEMPt
(3.13)
where
Ê t = estimated electricity energy consumption
Similarly, the error in month t–1 is specified
z t 1 = E t 1  Eˆ t 1 = E t 1  A  A1Pt 1  A2 M1t 1  A3TEMPt 1
(3.14)
and the difference in errors between the two months may be specified by
z t = z t  z t 1 = E t  Eˆ t 1 = E t 1  A1  Pt  Pt 1   A 2  M1t  M1t 1 
A3  TEMPt  TEMPt 1 
Julian I. Silk and Frederick L. Joutz, “Short and long–run elasticities in US residential electricity
demand: a co–integration approach”, Energy Economics 19(1997), pp.493–513
16
29
or
z t = E t  A1Pt  A 2 M1t  A3TEMPt
(3.15)
Campbell and Perron has proposed three approaches17 in determining the
specification of z t . In the first approach, z t is specified by the series
j
z t = az t 1 +  bi z t i + ε t
(3.16)
i=1
The number of lags in (3.16) is determined by the autocorrelation criteria. The
selected number of lags is the number that removes autocorrelation between the error
terms so that the remaining error term ε t is completely random with zero expected
value.
In the second approach, a constant is added to (3.16) in the form
j
z t = C + az t 1 +  bi z t i + ε t
(3.17)
i=1
In the third approach, a time trend is added to capture effects of the potentially
significant trend variables
j
z t = C + az t 1 +  bi z t i + ct + ε t
(3.18)
i=1
3.2.3
Model Specification
Silk and Frederick has proposed a test to select the model specification
between (3.15)–(3.17). 1 8  For the case of Thailand, the Silk and Frederick tests will
not be applied to select the model specification. Instead, it is proposed to select the
model specification by applying the BJ and the EC techniques in the following
sequence. From the general model specification
j
E t = A + A1Pt + A 2 M1t + A3Temp t +  bi E t i + z t
(3.19)
i=1
where
j
z t = E t  Eˆ t +  gi z t i + ε t
i=1
17
18
Ibid., page 500
Loc.cit., page 501
(3.20)
30
there are three major components explaining the variations in E t . The first component
consists of the exogenous variables Pt , M1t , and Temp t . The autoregressive term
j
 bi E t i is the second component, and the error correction term z t is the third
i=1
component of the model. Two approached may be used to estimate the (3.19) modek.
In the first approach, electricity energy consumption is detrended by its own time
series. This approach will be referred to as the nondetrend method. Alternatively,
electricity energy consumption may be detrended by an exogenous variable such as
M1 , or by a time variable. This approach will be referred to as the M1 detrend
method and the time detrend method.
3.2.4
Nondetrend Method
The time series of electricity energy consumption are analyzed for
autocorrelations and partial autocorrelations by the BJ technique. The stationary forms
of the series for the four regions of EGAT, PEA, and MEA are identified and
specified as
EGAT
1  B 1  B12  EGATt
1  B 1  B12  CENTRALt
1 + 0.5417B + 0.3722B
2


= 0.2300 + 1  0.5187B 1  0.6813B12 u t




+ 0.1563B3 1  B 1  B12 NORTHEASTt
= 0.3375 + 1  0.4815 u t
1 + 0.4058B 1 + 0.5910B12 + 0.3384B24  1  B 1  B12 SOUTHt


= 0.0785 + 1+0.2169B11 u t
1 + 0.5750B + 0.3561B
2



+ 0.1881B3 1  B 1  B12 NORTHt


= 0.2417 + 1  0.6396B12 u t
MEA
1  B 1  B12  MEAt


=  0.5095 + 1  0.5302B 1  0.8657B12 u t
PEA
1  B 1  B12  PEAt

=  0.0575 + 1  0.5108B 1  0.7346B12 u t


= 0.1886 + 1  0.6028B 1  0.5663B12 u t
31
3.2.5
M1 and Time Detrend Method
The exogenous variable M1 is used to detrend the electricity energy demand
by regressing electricity energy demand on M1. Series of the differences between
actual and estimated electricity energy consumption are then identified for the AR and
MA terms by the BJ technique. The patterns of AR and MA are then used as
guidelines for the specification of the electricity energy demand model. Alternatively,
a time variable may be used to detrend the electricity energy demand in the same
manners as the M1 variable.
The M1 regression results for the three power authorities are summarized
below
EGAT
EGATt = 1,928.7580 + 0.0117M1t 1
adj  R 2 = 0.9089
(t = 15.06) (t = 38.82)
CENTRAL t = 1,692.2730 + 0.0084M1t 1
(t = 17.29)
adj  R 2 = 0.8977
(t = 36.42)
NORTHEASTt = 55.0927 + 0.0012M1t 1
adj  R 2 = 0.9035
(t = 3.93) (t = 37.61)
SOUTH t = 84.8092 + 0.0010M1t 1
adj  R 2 = 0.9402
(t = 9.50) (t = 48.76)
NORTH t = 96.5830 + 0.0010M1t 1
adj  R 2 = 0.8834
(t = 7.35) (t = 33.84)
MEA
MEA t = 1,349.2320  0.0021M1 + 0.0050M1t 2
adj  R 2 = 0.8183
(t = 28.63) (t = –3.12) (t = 7.27)
PEA
PEA t = 483.0679 + 0.0080M1t 2
adj  R 2 = 0.9329
(t = 6.17) (t = 44.30)
Series of the differences between actual and estimated electricity energy
consumption are then identified for the AR and MA terms by the BJ technique. The
identification results from the software PROC ARIMA in SAS/ETS for the three
power authorities are summarized below.
32
EGAT
1  0.8487B 1  0.9747B12  EGATt


=  0.6152 + 1  0.3616B 1  0.6619B12 u t
1  0.5356B  0.2075B 1  0.9755B  CENTRAL =  0.6785 + 1  0.6847B  u
1  0.6133B 1  0.7194B  NORTHEAST =  1.0672 + 1 + 0.2115B  u
1  0.8849B 1  0.9676B  SOUTH =  0.03691 + 1  0.4305B 1  0.0683B  u
1  0.9029B 1  0.9805B  NORTH =  0.0215 + 1  0.4337B 1  0.7038B  u
2
12
12
t
12
t
17
t
t
12
12
t
t
12
12
t
t
MEA
1  0.3264B  0.2231B 1  0.6190B  MEA
2
12
t
=  4.8132 + u t
PEA
1  0.3912B  0.2592B 1  0.9130B  PEA
2
12
t


=  1.9078 + 1  0.5783B12 u t
When time is used as the detrend variable, electricity energy consumption is
regressed on time with the following results
EGAT
EGATt = 3,904.0808 + 35.4386TIME t
(t = 49.86)
adj  R 2 = 0.9139
(t = 40.18)
CENTRAL t = 3,117.9401 + 25.2871TIME t
adj  R 2 = 0.8930
(t = 49.50) (t = 35.64)
NORTHEASTt = 261.3636 + 3.8005TIME t
adj  R 2 = 0.9344
(t = 36.06) (t = 46.55)
SOUTH t = 255.1707 + 3.1359TIME t
adj  R 2 = 0.9682
(t = 62.40) (t = 68.07)
NORTH t = 269.6064 + 3.2151TIME t
adj  R 2 = 0.9160
(t = 38.46) (t = 40.72)
MEA
MEA t = 1,818.5050 + 8.4902TIME t
(t = 52.88) (t = 21.92)
adj  R 2 = 0.7592
33
PEA
adj  R 2 = 0.9480
PEA t = 2,011.1310 + 24.3753TIME t
(t = 50.44)
(t = 51.09)
As in the case of M1, series of the differences between actual and estimated
electricity energy consumption are identified for the AR and MA terms by the BJ
technique. The results are summarized below
EGAT
1  0.4837B  0.3665B 1  0.9826B  EGAT =  0.1145 + 1 + 0.1347B + 0.1900B 
1  0.6743B  u
1  0.9467B 1  0.9882B  CENTRAL =  0.0270 + 1  0.4811B + 0.1405B 
1  0.7047B  u
1  0.4850B  0.2210B 1  0.9502B  NORTHEAST =  0.0378 + 1  0.5060B  u
1  0.9083B 1  0.9809B  SOUTH =  0.0020 + 1  0.4185B 1  0.1230B  0.6626B  u
1  0.4645B  0.2574B 1  0.9764B  NORTH =  0.0183 + 1  0.6429B  u
2
12
7
10
t
12
t
12
7
t
12
t
2
12
12
t
t
12
6
12
t
2
12
12
t
t
MEA
1  0.5144B  0.4016B 1  0.9942B  MEA
2
12
t


=  0.0154 + 1  0.8228B12 u t
PEA
1  0.4925B  0.2075B 1  0.6213B  PEA
2
12
t
=  0.2414 + u t
The AR and MA terms identified by the BJ technique may be used as
guidelines for electricity energy demand model specifications. The guidelines for
model specification are summarized in Table 3.1
t
34
Table 3.1
Identifications of AR and MA Terms
Nondetrend Method
Power
Authority
AR, month
M1 Detrend Method
EGAT
1, 12, 13
MA ,
month
1, 12, 13
CENTRAL
1, 12, 13
1, 12, 13
1
11
1, 12, 13
1, 12, 13
1, 12, 13
1, 6, 7, 12,
13
12
1, 12, 13
1, 12, 13
1, 2, 12,
13, 14
12
MEA
1, 2, 3, 4,
12, 13, 14,
15, 16
1, 2, 12,
13, 14, 24,
25, 26, 36,
37, 38
1, 2, 3, 4,
12, 13, 14,
15, 16
1, 12, 13
1, 2, 12,
13, 14
1, 12, 13
1, 12, 13
–
1, 12, 13
1, 12, 13
1, 2, 12,
13, 14
1, 2, 12,
13, 14
12
PEA
1, 2, 12,
13, 14
1, 2, 12,
13, 14
NORTHEAST
SOUTH
NORTH
AR, month
12
7
1, 2, 12,
13, 14
1, 12, 13
MA ,
month
1, 12, 13
Time Detrend Method
12
AR, month
1, 2, 12,
13, 14
1, 12, 13
MA ,
month
7, 10, 12,
19, 22
1, 7, 12,
13, 19
12
–
3.3 Model for Electricity Energy Consumption
Data on electricity energy consumption are collected from EGAT, MEA for
the period January 1991 through September 2003. The PEA data are available only
for the period October 1991 through September 2003. Electricity energy consumption
at the EGAT level will be modeled for all of the regions, the central region, the
northeastern region, the northern region, and the southern region. Due to constraints
on the data availability, the MEA and PEA models will not be disaggregated into
regions.
3.3.1
Nondetrend Model
From the correlation analysis of EGAT electricity energy consumption and the
M1 at various lags it is found that the pairwise correlation of the M1 at lag 1 and
electricity energy is higher the others. The M1 at lag 1 is then selected to be one of
the exogenous variables in the forecasting model of EGAT electricity energy
consumption.
EGAT
The forecasting model of EGAT electricity energy consumption may be
written in the form
EGATt = A + A1EGATt 1 + A 2 EGATt 12 + A3EGATt 13 + A9 M1t 1 + A10TEMPt
+ A11PRICE t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.21)
35
where TEMPt is the mean of the cumulative average daily temperature in Thailand in
month t and PRICE t is the average consumer electricity price per KWh in month t.
The forecasting model of EGAT electricity energy consumption in the central
region may be written as
CENTRAL t = A + A1CENTRAL t 1 + A 2CENTRAL t 12 + A3CENTRAL t 13 + A9 M1t 1
+ A10TEMP_Ct + A11PRICE_PEA t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.22)
where TEMP_Ct is the mean of the cumulative average daily temperature in month t
in the central region of PEA distribution system and PRICE_PEA t is the average PEA
consumer electricity price per KWh in month t
In the northeast region, the forecasting model of EGAT electricity energy
consumption can be written as
NORTHEASTt = A + A1NORTHEASTt 1 + A 2 NORTHEASTt 2 + A 3 NORTHEASTt 3
+ A 4 NORTHEASTt 4 + A5 NORTHEASTt 12 + A6 NORTHEASTt 13
+ A7 NORTHEASTt 14 + A8 NORTHEASTt 15 + A9 NORTHEASTt 16
+ A10 M1t 1 + A11TEMP_NE t + A12 PRICE_PEA t + z t
z t = θ1z t 1 + ε t
(3.23)
where TEMP_NE t is the mean of the cumulative average daily temperature in month t
in the northeast region of PEA distribution system.
The forecasting model of EGAT electricity energy consumption in the south
region may be written as
SOUTH t = A + A1SOUTH t 1 + A 2SOUTH t 2 + A 3SOUTH t 12 + A 4SOUTH t 13
+ A5SOUTH t 14 + A 6SOUTH t 24 + A 7SOUTH t 25 + A8SOUTH t 26
+ A9SOUTH t 36 + A10SOUTH t 37 + A11SOUTH t 38 + A12 M1t 1
+ A13TEMP_St + A14 PRICE_PEA t + z t
z t = θ11z t 11 + ε t
(3.24)
where TEMP_St is the mean of the cumulative average daily temperature in month t
in the south region of PEA distribution system.
Finally the forecasting model of EGAT electricity energy consumption in
month t in the north region may be written in as
36
NORTH t = A + A1NORTH t 1 + A 2 NORTH t 2 + A 3 NORTH t 3 + A 4 NORTH t 4
+ A5 NORTH t 12 + A 6 NORTH t 13 + A 7 NORTH t 14 + A8 NORTH t 15
+ A9 NORTH t 16 + A10 M1t 1 + A11TEMP_N t + A12 PRICE_PEA t + z t
z t = θ12 z t 12 + ε t
(3.25)
where TEMP_N t is the mean of the cumulative average daily temperature in month t
in the north region of PEA distribution system.
Similarly, from the regression analysis, the M1 at lag 0 and lag 2 are selected
to be the exogenous variables i the forecasting model of MEA electricity energy
consumption and the M1 at lag 2 is the exogenous variable in the forecasting model of
PEA electricity energy consumption.
MEA
The forecasting model of MEA electricity energy consumption may be written
in the form
MEA t = A + A1MEA t 1 + A 2 MEA t 12 + A3MEA t 13 + A 4 M1t
+ A5 M1t 2 + A6 TEMP_C t + A 7 PRICE_MEA t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.26)
PEA
The forecasting model of PEA electricity energy consumption may be written
as
PEA t = A + A1PEA t 1 + A 2 PEA t 12 + A3PEA t 13 + A 4 M1t 2
+ A 6 TEMP + A 7 PRICE_PEA t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.27)
The parameters in the forecasting models are estimated by PROC Model in
SAS software. The equation in forecasting model of EGAT electricity energy
consumption can be written as
37
EGATt =  430.0440 + 0.7129EGATt 1 + 0.7754EGATt 12  0.6407EGATt 13
(t = –2.24) (t = 13.32)
(t = 15.35)
(t = –9.32)
+ 0.0021M1t 1 + 1.1989TEMPt  160.0250PRICEt + zˆ t
(t = 4.96)
(t = 4.72)
(t= –1.57)
ẑ t =  0.3769z t 1  0.3792z t 12  0.2196z t 13
(t = –4.31) (t= –3.83)
where adj  R 2 = 0.9850 .
(t = –2.20)
The signs of an exogenous variables are correct as expected. The price
variable has the correct sign and is not significant at 0.5 significant level but is
significant at 0.13 significant level. The parameters of part errors Z t 1 , Z t 12 and Z13
are significant and can be used the error–correction model.
The equations of forecasting models are summarized in Table 3.2
Table 3.2
Estimation Results of Nondetrend Electricity energy Consumption
Model by Power Authorities
EGAT : adj  R 2 = 0.9850
EGATt =  430.0440 + 0.7129EGATt 1 + 0.7754EGATt 12  0.6407EGATt 13
(t = –2.24) (t = 13.32)
(t = 15.35)
(t = –9.32)
+ 0.0021M1t 1 + 1.1989TEMPt  160.0250PRICEt + zˆ t
(t = 4.96)
(t = 4.72)
(t= –1.57)
ẑ t =  0.3769z t 1  0.3792z t 12  0.2196z t 13
(t = –4.31) (t= –3.83)
(t = –2.20)
EGAT Central : adj  R 2 = 0.9803
CENTRAL t =  545.6500 + 0.6868CENTRAL t 1 + 0.7170CENTRAL t 12
(t = –2.53) (t = 12.60)
(t = 13.15)
0.5873CENTRAL t 13 + 0.0019M1t 1 + 1.3475TEMP_Ct
(t = –8.59)
(t = 5.29)
210.2510PRICE_PEA t + zˆ t
(t = –2.14)
ẑ t =  0.3106z t 1 + 0.2414z t 12
(t = –3.58) (t = –2.54)
(t = 4.87)
38
Table 3.2
(Continued)
EGAT Northeast : adj  R 2 = 0.9846
NORTHEASTt = 0.0412 + 0.2612NORTHEASTt 1 + 0.1941NORTHEASTt 3
(t = 1.17) (t = 3.55)
(t = 2.72)
+ 0.8621NORTHEASTt 12  0.2344NORTHEASTt 13
(t = 21.45)
(t = –2.99)
0.2035NORTHEASTt 15 + 0.0003M1t 1 + 0.1140TEMP_NE t
(t = –2.75)
(t = 5.90)
(t = 5.69)
74.6667PRICE_PEA t + zˆ t
(t = –4.68)
ẑ t =  0.3047z t 12
(t = –3.08)
EGAT South : adj  R 2 = 0.9895
SOUTH t =  205.6990 + 0.3448SOUTH t 1 + 0.2403SOUTH t 2
(t = –4.95) (t = 4.96)
(t = 4.96)
+ 0.4449SOUTH t 12  0.4438SOUTH t 13 + 0.2490SOUTH t 24
(t = 6.31)
(t = –6.59)
(t = 4.55)
+ 0.0001M1t 1 + 0.2831TEMP_St + 4.6599PRICE_PEAt + zˆ t
(t = 4.42)
(t = 5.96)
(t = 0.35)
39
Table 3.2
(Continued)
EGAT North : adj  R 2 = 0.9821
NORTH t =  132.0760 + 0.2219NORTH t 1 + 0.1450NORTH t 2
(t = –4.25) (t = 3.05)
(t = 3.25)
+ 0.6065NORTH t 12  0.2322NORTH t 13  0.0003M1t 1
(t = 11.26)
(t = –3.24)
(t = 6.84)
+ 0.2252TEMP_N t  13.0464PRICE_PEA t + zˆ t
(t = 7.53)
(t = –0.73)
MEA : adj  R 2 = 0.9616
MEA t =  276.8910  181.8220PRICE_MEA t + 0.6314MEA t 1 + 0.5108MEA t 12
(t = –2.40) (t = –4.09)
(t = 12.77)
(t = 9.00)
0.4283MEA t 13 + 1.0642TEMP_Ct + zˆ t
(t = 7.02)
(t = 7.01)
ẑ t =  0.3183z t 1
(t = –3.49)
PEA : adj  R 2 = 0.9842
PEA t =  759.1100 + 0.5505PEA t 1 + 0.1654PEAt 12 + 0.0021M1t 2
(t = –3.68) (t = 9.64)
(t = 3.02)
+ 22.1426PRICE_PEA t + 1.1862TEMPt + zˆ t
(t = 0.23)
ẑ t =  0.3314z t 1 + 0.2442z t 12
(t = –3.71) (t = 2.51)
(t = 5.77)
(t = 7.58)
40
3.3.2 Detrend Model: M1
The forecasting models of electricity consumptions can be written in the form
EGAT
EGATt = A + A1EGATt 1 + A 2 EGATt 12 + A3EGATt 13 + A 4 M1t 1 + A5TEMPt
+ A 6 PRICE t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.28)
EGAT : Central
CENTRAL t = A + A1CENTRAL t 1 + A 2CENTRAL t 2 + A3CENTRAL t 12
+ A 4 CENTRAL t 13 + A5CENTRAL t 14 + A 6 M1t 1 + A 7 TEMP_C t
+ A8 PRICE_PEA t + z t
z t = θ12 z t 12 + ε t
(3.29)
EGAT : Northeast
NORTHEASTt = A + A1NORTHEASTt 1 + A 2 NORTHEASTt 12
+ A3 NORTHEASTt 13 + A 4 M1t 1 + A5TEMP_NE t
+ A6 PRICE_PEA t + z t
z t = θ 7 z t 7 + ε t
(3.30)
EGAT : South
SOUTH t = A + A1SOUTH t 1 + A 2SOUTH t 12 + A3SOUTH t 13 + A 4 M1t 1
+ A5TEMP_St + A 6 PRICE_PEA t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.31)
41
EGAT : North
NORTH t = A + A1NORTH t 1 + A 2 NORTH t 12 + A 3 NORTH t 13 + A 4 M1t 1
+ A5TEMP_N t + A6 PRICE_PEA t + z t
z t = θ1z t 1 + θ12 z t 12 + θ13z t 13 + ε t
(3.32)
MEA
MEA t = A + A1MEA t 1 + A 2 MEA t 2 + A3MEA t 12 + A 4 MEA t 13 + A5MEA t 14
+ A6 M1t + A 7 M1t 2 + A8TEMP_C t + A9 PRICE_MEA t + ε t
(3.33)
PEA
PEA t = A + A1PEA t 1 + A 2 PEA t 2 + A3PEA t 12 + A 4 PEA t 13 + A 5PEA t 14
+ A6 M1t 2 + A7 TEMPt + A8 PRICE_PEA t + z t
z t = θ12 z t 12 + ε t
(3.34)
Estimations of the M1 detrend model for the three power authorities are
summarized in Table 3.3.
Table 3.3
Estimation Results of M1 Detrend Electricity energy Consumption
Model by Power Authorities
EGAT : adj  R 2 = 0.9850
EGATt =  430.0440 + 0.7129EGATt 1 + 0.7754EGATt 12  0.6407EGATt 13
(t = –2.24) (t = 13.32)
(t = 15.35)
(t = –9.32)
+ 0.0021M1t 1 + 1.1989TEMPt  160.0250PRICEt + zˆ t
(t = 4.96)
(t = 4.72)
ẑ t =  0.3769z t 1  0.3792z t 12  0.2196z t 13
(t = –4.31) (t = –3.83)
(t = –2.20)
(t = –1.52)
42
Table 3.3
(Continued)
EGAT Central : adj  R 2 = 0.9825
CENTRAL t =  1,063.6700 + 0.3444CENTRAL t 1 + 0.3209CENTRAL t 2
(t = –4.22) (t = 4.84)
(t = 4.53)
+ 0.6274CENTRAL t 12  0.3364CENTRAL t 13
(t = 10.27)
(t = –4.56)
0.1742CENTRAL t 14 + 0.0023M1t 1 + 2.0572TEMP_Ct
(t = –2.19)
(t = 5.58)
(t = 6.40)
237.3940PRICE_PEA t + zˆ t
(t = –2.08)
ẑ t =  0.2757z t 12
(t = –2.52)
EGAT Northeast : adj  R 2 = 0.9840
NORTHEASTt =  96.2250 + 0.3307NORTHEASTt 1 + 0.7160NORTHEASTt 12
(t = –2.78) (t = 4.95)
(t = 14.34)
0.2617NORTHEASTt 13 + 0.0003M1t 1 + 0.1917TEMP_NE t
(t = –3.62)
31.9091PRICE_PEA t
(t = –1.53)
(t = 6.85)
(t = 6.31)
43
Table 3.3
(Continued)
EGAT South : adj  R 2 = 0.9906
SOUTH t =  32.4147 + 0.7879SOUTH t 1 + 0.9225SOUTH t 12
(t = –1.47) (t = 14.02)
(t = 18.72)
0.7687SOUTH t 13 + 0.0001M1t 1 + 0.0503TEMP_St
(t = –10.86)
(t = 2.58)
(t = 2.00)
+ 0.5819PRICE_PEA t + zˆ t
(t = 0.08)
ẑ t =  0.3599z t 1  0.4353z t 12  0.2773z t 13
(t = –4.01) (t = –4.55)
(t = –2.85)
EGAT North : adj  R 2 = 0.9811
NORTH t =  90.5757 + 0.4793NORTH t 1 + 0.6462NORTH t 12
(t = –3.49) (t = 6.40)
(t = 11.66)
0.3411NORTH t 13 + 0.0002M1t 1 + 0.1621TEMP_N t
(t = –4.16)
(t = 6.11)
(t = 6.22)
9.9956PRICE_PEA t + zˆ t
(t = –0.66)
ẑ t =  0.2435z t 1
(t = –2.31)
PEA : adj  R 2 = 0.9842
PEA t =  831.9630 + 0.3112PEA t 1 + 0.1878PEAt 2 + 0.3991PEA t 12
(t = –3.55) (t = 4.05)
(t = 3.16)
(t = 5.26)
0.1675PEA t 13 + 0.0020M1t 2 + 1.2988TEMPt
(t = –2.08)
(t = 6.11)
+ 14.6278PRICE_PEA t
(t = 0.12)
(t = 5.79)
44
3.3.3
Detrend Model: Time
The forecasting models of electricity consumption may be written as
EGAT
EGATt = A + A1EGATt 1 + A 2 EGATt 2 + A3EGATt 12 + A 4 EGATt 13 + A5EGATt 14
+ A5TIME t + A 6 TEMPt + A 7 PRICE t + z t
z t = θ7 z t 7 + θ10 z t 10 + θ12 z t 12 + θ19 z t 19 + θ 22 z t 22 + ε t
(3.35)
EGAT : Central
CENTRAL t = A + A1CENTRAL t 1 + A 2CENTRAL t 12 + A3CENTRAL t 13
+ A 4TIME t + A5TEMP_C t + A 6 PRICE_PEA t + z t
z t = θ1z t 1 + θ7 z t 7 + θ12 z t 12 + θ13z t 13 + θ19 z t 19 + ε t
(3.36)
EGAT : Northeast
NORTHEASTt = A + A1NORTHEASTt 1 + A 2 NORTHEASTt 2
+ A3 NORTHEASTt 12 + A 4 NORTHEASTt 13 + A5 NORTHEASTt 14
+ A6 TIME t + A 7 TEMP_NE t + A8PRICE_PEA t + z t
z t = θ12 z t 12 + ε t
(3.37)
EGAT : South
SOUTH t = A + A1SOUTH t 1 + A 2SOUTH t 12 + A 3SOUTH t 13 + A 4TIME t
+ A5TEMP_St + A 6 PRICE_PEA t + z t
z t = θ1z t 1 + θ6 z t 6 + θ7 z t 7 + θ12 z t 12 + θ13z t 13 + ε t
(3.38)
45
EGAT : North
NORTH t = A + A1NORTH t 1 + A 2 NORTH t 2 + A3 NORTH t 12 + A 4 NORTH t 13
+ A5 NORTH t 14 + A6TIME t + A 7 TEMP_N t + A8PRICE_PEA t + z t
z t = θ12 z t 12 + ε t
(3.39)
MEA
MEA t = A + A1MEA t 1 + A 2 MEA t 2 + A3MEA t 12 + A 4 MEA t 13 + A5MEA t 14
+ A6 TIME t + A7 TEMP_Ct + A8 PRICE_MEA t + z t
z t = θ12 z t 12 + ε t
(3.40)
PEA
PEA t = A + A1PEA t 1 + A 2 PEA t 2 + A3PEA t 12 + A 4 PEA t 13 + A 5PEA t 14
+ A6 TIME t + A7 TEMPt + A8 PRICE_PEA t + ε t
(3.41)
Estimations of the time detrend model for the three power authorities are
summarized in Table 3.4.
Table 3.4
Estimation Results of Time Detrend Electricity energy Consumption
Models by Power Authorities
EGAT : adj  R 2 = 0.9853
EGATt = 280.2028 + 0.3329EGATt 1 + 0.3516EGATt 2 + 0.7127EGATt 12
(t = 0.69) (t = 4.42)
(t = 4.86)
(t = 11.71)
0.3868EGATt 13  0.3082EGATt 14 + 14.9263TIME
(t = –5.01)
(t = –4.03)
+ 2.2613TEMPt  649.9750PRICE + zˆ t
(t = 5.60)
(t = –2.57)
ẑ t = 0.1845z t 7 + 0.2030z t 10  0.2419z t 12
(t = 2.09)
(t = 2.32)
(t = –2.36)
(t = 4.49)
46
Table 3.4
(Continued)
EGAT Central : adj  R 2 = 0.9792
CENTRAL t = 51.1803 + 0.8732CENTRAL t 1 + 0.8580CENTRAL t 12
(t = 0.24) (t = 24.69)
(t = 19.07)
0.8602CENTRAL t 13 + 4.9390TIME + 0.8612TEMP_Ct
(t = –17.70)
(t = 3.09)
(t = 3.55)
265.9370PRICE_PEA t + zˆ t
(t = –1.88)
ẑ t =  0.4279z t 1  0.4683z t 12  0.2667z t 13
(t = –5.25) (t = –5.26) (t = –2.80)
EGAT Northeast : adj  R 2 = 0.9885
NORTHEASTt =  75.0712 + 0.3392NORTHEASTt 1 + 0.1347NORTHEASTt 2
(t = 2.00) (t = 5.21)
(t = 2.08)
+ 2.3671TIME + 0.3807TEMP_NE t  65.2448PRICE_PEA t + zˆ t
(t = 8.78)
(t = 9.62)
(t = –3.36)
ẑ t = 0.8443z t 12
(t = 15.42)
EGAT South : adj  R 2 = 0.9917
SOUTH t =  29.3433 + 0.7997SOUTH t 1 + 0.8341SOUTH t 12
(t = –1.38) (t = 17.99)
(t = 15.09)
0.8375SOUTH t 13 + 0.8572TIME + 0.1477TEMP_St
(t = –14.74)
(t = 4.62)
(t = 4.14)
31.8448PRICE_PEA t + zˆ t
(t = –3.15)
ẑ t =  0.3992z t 1  0.1687z t 6  0.4256z t 12  0.2649zt 13
(t = –4.67) (t = –2.22) (t = –4.43)
(t = –2.80)
47
Table 3.4
(Continued)
EGAT North : adj  R 2 = 0.9872
NORTH t =  76.8115 + 0.2605NORTH t 1 + 0.1396NORTH t 2
(t = –2.21) (t = 4.09)
(t = 2.25)
+ 2.3190TIME + 0.3970TEMP_N t  60.0873PRICE_PEA t + zˆ t
(t = 9.54)
(t = 10.62)
(t = –3.48)
z t = 0.8128z t 12
(t = 13.60)
MEA : adj  R 2 = 0.9602
MEA t =  27.8191 + 0.4026MEA t 1 + 0.3921MEA t 2 + 0.6602MEA t 12
(t = –0.16) (t = 5.59)
(t = 5.60)
(t = 11.05)
0.3897MEA t 13 + 0.3135MEA t 14 + 4.5058TIME
(t = –5.28)
(t = –4.27)
(t = 4.61)
+ 1.1600TEMP_Ct  328.1980PRICE_MEA t + zˆ t
(t = 6.30)
(t = –3.46)
z t =  0.2577z t 12
(t = –2.42)
PEA : adj  R 2 = 0.9821
PEA t =  254.4270 + 0.5691PEA t 1 + 0.4142PEA t 12  0.3280PEA t 13
(t = –0.78) (t = 8.83)
(t = 5.11)
(t = –4.04)
+ 10.9533TIME + 1.8337TEMPt  394.4580PRICE_PEA t
(t = 4.76)
(t = 6.17)
(t = –2.17)
3.4 Summary of Estimation Results
Three different electricity energy consumption model specifications :
nondtrend, M1 detrend, and time detrend, have been estimated and tested for the case
of Thailand. All of the three specifications have high explanatory power. The adjusted
R2 for the nondetrend models range from 0.9616 to 0.9895. The error correction terms
48
are found to enhance the explanatory power of the detrend model significantly, with
the exception of model for EGAT south, EGAT north, and PEA.
Non–price exogenous variables in the nondetrend models have expected signs
that are statistically significant at the 0.05 level. The price variable has expected sign
and is significant at the 0.05 level for the EGAT central, the EGAT northeast, and the
MEA models. The remaining nondetrend models have expected price signs that are
not significant with the exception of the EGAT south and the PEA models, where the
price signs are positive but not statistically significant.
The adjusted R2 for the M1 detrend models are between 0.9678 to 0.9906. The
error correction terms enhance the explanatory power of all models significantly,
except for the EGAT northeast, MEA, and PEA models. The statistically significant
non- price variables have expected signs. The price variable has the expected negative
sign but significant only for the EGAT central and MEA models. The exception is the
EGAT south and the PEA models where the price variable has positive sign but not
statistically significant.
The adjusted R2 for the time detrend models range from 0.9602 to 0.9917. The
error correction terms are found to enhance the explanatory power of the models
significantly, except for the PEA model. The statistically significant non-price
variables have the expected signs. The price variable has the expected negative sign
which is significant at the 0.005 level for all models.
Table 3.5 compares the model errors between the nondetrend, the M1 detrend,
and the time detrend models. The errors of the three types of models are compatible
although the standard deviations of the errors of the M1 detrend model and the time
detrend models are slightly lower than the nondetrend model. Nevertheless, the errors
of all the three types of model are less than three percent.
The modeling exercises suggest that the model for electricity energy
consumption may have the following two specifications
3
E t = CON +  Ai E t i + T*TEMPt +  M jM1t  j + P*PRICE t 1 + u t
(3.42)
Et = CON +  Ai Et i + T*TEMPt + B*t + P*PRICE t 1 + u t
(3.43)
iI
j=0
iI
where i is the set of lagged variables determined from the BJ technique, and u t is the
residual E t  Eˆ t which is the error correction term in the model.
The foregoing modeling exercises are all in linear forms. In the next chapter,
the double log specification will be considered as a potential forecasting model. The
double log specification has an advantage over the linear specification in that the
model can provide the variable elasticities directly.
The modeling exercise suggests that there may be collinearity among the
autoregressive variable E t i . In order to alleviate the collinearity problem, it is
proposed to determine the number of autoregressive variables by the following
procedure. From the BJ autoregressive model which can be specified generally as
E t = a 0 +  a t i E t i + ε t
iI
(3.44)
49
where I is the set of lagged variables identified by the BJ technique, and  t is the
remaining random error with zero expected value, only the autoregressive variables
that are statistically significant will be retained in the model. The removal of
nonsignificant variables would increase the explanatory of (3.44) by increasing its the
adjusted R2. The selected variables will be specified as the autoregressive term in the
electricity energy consumption model.
Since collinearity may also exist in the electricity energy demand model, its
severity may be further reduced by taking into account the seasonal effect by
considering the signs of the autoregressive variables such as E t 12 and
E t  24 , E t 1 , E t 13 and E t  25 . If these variables have the same signs, the number of the
autoregressive variables may be reduced further to potentially increase the adjusted
R2 .
Granges et. al modeled the consumption of electricity energy in the US and
found the month variables to be significant. It is proposed that the month variables are
specified as dummy variables in the electricity energy consumption model for
Thailand. The proposed general form of the model may thus be specified as
nE t = f

nE t i ; i  Is , nTEMPt , nPt 1 , nM t  j ; j = 0, 1, 2, 3,
FEB, MAR, APR, MAY, JUN, JUL, AUG, SEP, OCT,
NOV, DEC 
(3.45)
nE t = f  nE t i ; i  Is , nTEMPt , nPt 1 , t, FEB, MAR, APR,
MAY, JUN, JUL, AUG, SEP, OCT, NOV, DEC 
(3.46)
Table 3.5
Model
EGAT
EGAT central
EGAT
northeast
EGAT south
EGAT north
MEA
PEA
Comparison of Errors between Nondetrend, M1 detrend, and Time Detrend Models
Nondetrend Model
M1 Detrend Model
adj.R2
error
Relative error adj.R2
error
Relative error
Mean
SD
Mean
SD
Mean
SD
Mean
SD
adj.R2
Time detrend Model
error
Relative error
Mean
SD
Mean
SD
0.9850
0.9803
0.9846
–0.4707
–0.1826
–0.1451
172.7385
142.8049
18.9675
0.0195
0.0221
0.0245
0.0162
0.0164
0.0187
0.9850
0.9825
0.9840
–0.4707
–0.6389
0.0000
173.3587
132.1482
19.7737
0.0200
0.0210
0.0267
0.0162
0.0153
0.0204
0.9853
0.9792
0.9885
0.8770
0.6957
–0.4871
168.0132
146.2536
18.0601
0.0195
0.0226
0.0279
0.0151
0.0189
0.0242
0.9895
0.9821
0.9616
0.9842
0.0000
0.0000
0.1025
0.0826
11.6963
17.6736
71.1919
114.8053
0.0164
0.0254
0.0233
0.0202
0.0133
0.0195
0.0156
0.0210
0.9960
0.9811
0.9678
0.9842
–0.0240
0.0036
0.0000
0.0000
12.0356
18.1669
65.2493
113.8868
0.0172
0.0262
0.0214
0.0207
0.0140
0.0200
0.0151
0.0267
0.9917
0.9872
0.9602
0.9821
0.0675
–0.2855
–0.2013
0.0000
11.2607
16.2315
70.4354
121.7313
0.0162
0.0252
0.0225
0.0226
0.0132
0.0225
0.0169
0.0288
50