Chapter 7
Forecasting of Exogenous Variables
7.1 Introduction
The following exogenous variables are used as exogenous variables to explain
variations in the electricity energy consumption model and in the maximum demand
model as presented in chapter 4, 5, and 5.
1. money supply in the narrow sense, M1
2. temperature in the kingdom, TEMPt , central region temperature,
TEMPtC , northeastern region temperature TEMPtNE , northern region temperature,
TEMPtN and southern region temperature, TEMPtS
3. amount of rainfall in the kingdom, RAIN t , and by regions, RAIN Ct ,
RAIN tNE , RAIN tN and RAIN St
4. number of customers in the MEA and PEA system
5. average electricity prices in the MEA and PEA system
The value of these exogenous variables will be forecasted in this chapter and
used as inputs for the electricity energy consumption model and the maximum
demand model.
7.2 Forecast of Money Supply, M1
When annual data on GDP at market prices and M1 between 1991 and 2003 in
Table 7.1 are analyzed for their relationship, the correlation coefficient between the
two variables is computed to be 0.97. This statistical exercise justifies the use of M1
as a proxy variable for GDP. The forecast of M1 are used as inputs in the forecast of
electricity energy consumption and maximum demand.
The VAR model is selected as a forecasting model for M1.The VAR model
may be specified generally as
M1t = CON +  M j*M1t Ji + G*GDP_CUR j + D 2 FEB + D3MAR + D 4 APR
i
+ D5 MAY + D6 JUN + D7 JUL + D8AUG + D9SEP + D10OCT + D11NOV
+ D12 DEC + u t
(7.1)
where GDP_CUR j is the GDP at market prices in year j which is related to t by
t =  j  1 *12 + m
The M1 series is identified by the BJ technique as
m = 1, 2, ..., 12
j = 1, 2, ...
(7.2)
100
1  B 1  B12  M1t


= δ + 1  θ1B 1  1B12 u t
(7.3)
The identification result suggests three autoregressive terms--- a one month lag, a 12
month lag, and a 13 month lag—that may be considered in the M1 forecasting model.
However, when the model is estimated with these AR terms, only the one month lag
AR term is found to be significant so the M1 model is respecified as
M1t = CON + M1*M1t 1 + G*GDP_CUR j + D 2 FEB + D3MAR + D 4 APR
+ D5 MAY + D6 JUN + D7 JUL + D8 AUG + D9SEP + D10OCT + D11NOV
+ D12 DEC + u t
(7.4)
Estimation results show that all of the coefficients except G are significant. Inspite of
the result, the GDP variable is retained in the model since its coefficient still has the
expected sign. The estimated M1 model with adjusted R2 of 0.9864 is presented
below
M1t =  16648.6000 + 0.9458M1t 1 + 0.0083GDP_CUR j + 7534.4430FEB
+ 2911.535MAR  892.3600APR + 2755.635MAY  9930.0200JUN
+ 2970.6930JUL + 11395.3300AUG + 2530.8100SEP + 13101.3400OCT
+ 11393.1000NOV + 33269.8700DEC
(7.5)
The (7.5) model is selected as the long term forecasting model. The (7.4)
model with the EC term is selected as the short term forecasting model. The short
term forecasting model with adjusted R2 of 0.9881 is presented below
M1t = PRE_M1t  0.4016u t 1 + 0.2182 t 10
(7.6)
PRE_M1t =  7618.9900 + 0.9950M1t 1 + 0.0019GDP_CUR1 + 5707.2070FEB
+ 1258.8790MAR  2031.9300APR + 1172.400MAY  11217.0000JUN
+ 2520.0310JUL + 10934.5200AUG + 2189.1750SEP
+ 10799.3800OCT + 9819.6240NOV + 30988.9200DEC
u t = AM1t  PRE_M1t
ε t = AM1t   PRE_M1t  0.4016u t 1 
(7.7)
(7.8)
(7.9)
The adjusted R 2 of the model is 0.9881 and AM1t is the actual value of M1t .
101
Table 7.1
Money supply in the Narrow Sense and GDP at market prices
Year
GDP
M1
2534
2,506,635
2,345,018
2535
2,830,914
2,807,214
2536
3,170,258
3,089,975
2537
3,634,496
3,709,759
2538
4,192,697
4,344,687
2539
4,622,832
4,898,449
2540
4,740,249
4,984,295
2541
4,628,431
4,885,745
2542
4,637,079
5,405,289
2543
4,923,263
5,937,535
2544
5,133,836
6,429,111
2545
5,451,854
7,220,588
2546
5,931,600
8,297,670
Source : NESDB, Bank of Thailand
7.3 Temperature Model
Monthly temperature used in the electricity energy consumption model and the
maximum demand model is the sum of the daily temperature in a given month. The
daily temperature is computed by the product of average daily temperature and the
number of days in a given month. Data on temperature are classified into the kingdom
temperature, TEMPt , the central region temperature, TEMPtC , the northeastern region
temperature, TEMPtNE , the northern region temperature, TEMPtN , and the southern
region temperature, TEMPtS .
The daily average temperature in the kingdom is computed from the sum of
daily average temperatures recorded at each recording station divided by the number
of recording stations in the kingdom. The regional average daily temperature for each
region is computed by the same method. The temperature data between January 1992
and December 2003 are used to estimate the temperature model which is specified as
TEMPtq = CON +  M i TEMPtqi + D 2 FEB + D3MAR + D 4 APR + D 5MAY
iIS
+ D6 JUN + D7 JUL + D8 AUG + D9SEP + D10OCT + D11NOV
+ D12 DEC + u t
(7.8)
where IS is the set index of lagged autoregressive terms to be identified by the BJ
technique.
Thailand Temperature Model, TEMPt
Thailand temperature series is identified by the BJ technique to be
102
1   B   B 1   B
2
1
2
12
1


 2 B24 1  B12 TEMPt = δ + u t
(7.9)
The identification results suggest the autoregressive terms with a one month lag, a 2
month lag, a 12 month lag, a 13 month lag, and a 36 month lag. However, when
model (7.8) is estimated with the suggested AR terms, only coefficients of the one
month lag and 2 month lag AR terms are significant, so the model is respecified as
TEMPt = 401.1444 + 0.2732TEMPt 1 + 0.2096TEMPt 2  37.8354FEB
+ 111.2587MAR + 90.9287APR + 68.0347MAY + 19.2652JUN
+ 44.4827JUL + 40.0873AUG + 1.9270SEP + 27.4957OCT
 27.9558NOV  30.5850DEC
(7.10)
The adjusted R2 of the model is 0.8968.
Central Region Temperature Model, TEMPtC
The central region temperature series is identified to be
1  1B 1  1B12  2 B24 1  B12  TEMPtC = δ + 1  θ1B u t
(7.11)
which suggests the autoregressive terms with a one month lag, a 12 month lag, and a
13 month lag. However, when model (7.8) is estimated with the suggested AR terms,
only coefficient of the one month lag is found to be significant, so the central
temperature model is respecified as
TEMPtC = 548.1182 + 0.3426TEMPtC1  54.1182FEB + 87.9070MAR + 48.4003APR
+ 56.2994MAY + 8.2773JUN + 41.3219JUL + 26.3771AUG  10.9820SEP
+ 22.1221OCT  27.2713NOV  20.9770DEC
(7.12)
The adjusted R2 of the model is 0.8242.
Northeastern Temperature Model, TEMPtNE
The northeastern region temperature series is identified to be
1  1B 1  1B12  2 B24 1  B12  TEMPtNE = δ + 1  θ1B u t
(7.13)
The series has the same identity as the central series. The estimated model is
presented below
103
TEMPtNE = 582.9611 + 0.2056TEMPtNE
1 + 50.8685FEB + 128.0494MAR
+ 153.8964APR + 121.6610MAY + 112.3199JUN + 102.7065JUL
+ 93.9235AUG + 83.3724SEP + 68.3865OCT + 18.5988NOV
 26.4507DEC
(7.14)
The adjusted R2 of the model is 0.8433.
Northern Temperature Model, TEMPtN
The northern temperature series is slightly different from the central and
northeastern temperature series. The northern temperature series is identified to be
1  1B 1  1B12  2 B24 1  B12  TEMPtN = δ + u t
(7.15)
When the suggested AR terms are included in the (7.8) specification for
estimations, the final specification selected is
TEMPtN = 465.7265 + 0.3560TEMPtN1 + 51.6370FEB + 125.6907MAR + 152.3891APR
+ 101.9170MAY + 95.9207JUN + 83.8206JUL + 77.8949AUG + 74.1777SEP
+ 60.3232OCT + 9.8031NOV  33.7543DEC
(7.16)
The adjusted R2 of the model is 0.8876.
Southern Temperature Model, TEMPtS
The southern temperature series is identified to be
1   B   B 1   B
2
1
2
12
1


 2 B12 1  B12 TEMPtS = δ + u t
(7.17)
When the suggested AR terms are included in the (7.8) specification for estimations,
the final specification selected is
TEMPtS = 371.1114 + 0.3714TEMPtS1 + 0.3304TEMPtS2  0.1456TEMPtS24
+ 20.3435FEB + 37.9485MAR + 47.4902APR + 21.9773MAY
+ 0.5286JUN + 0.2197JUL + 0.0102AUG  5.1822SEP  10.3517OCT
 13.9664NOV  23.7287DEC
(7.18)
104
7.4 Rainfall Model
Rainfall data are collected for the period between January 1991 and December
2003. Identification results of the rainfall series by the BJ technique are presented
below
Whole Kingdom
1  B  RAIN


= 35.4527 + 1 + 0.1347B  1  0.9997B12 u t
12
t
(7.19)
Central Region
1  B  RAIN
12
C
t


=  6.1873 + 1  0.8449B12 u t
(7.20)
Northeastern Region
1  0.1366B + 0.2327B 1 + 0.8096B
+ 1 + 0.2437B  u
8
12

+ 0.3661B24 RAIN tNE = 2.3157
13
t
(7.21)
Northern Region
1 + 0.5146B
12




+ 0.3590B24 1  B12 RAIN tN = 32.0303 + 1  0.1835B9 u t
(7.22)
Southern Region
1  0.3185B 1  0.6368B12 1  B12  RAINSt = 1245.1170


+ 1  0.2301B9 + 0.3092B11 u t
(7.23)
The amount of rainfall forecast from (7.19)–(7.23) are monthly forecast. These
monthly forecast must be transformed into annual forecast since the forecasting model
of the agricultural pumping group which requires the amount of rainfall forecast as an
input is an annual model.
7.5 Number of Electricity Customers Model
Data on the number of electricity customers are annual data between 1992 and
2003. The number of electricity customers will be forecasted by a simple linear time
trend model
CUSijr = CON + Ti *j
(7.24)
105
where CUSijr = number of i th group customers in year j (j=1 for 1992, 2 for
1993…….)
CON = constant
Ti = rate of average annual increase of the i customer group.
j = 1 for 1992, 2 for 1993, 3 for 1994, …
Estimation results of the model is summarized in Table 7.2
Table 7.2
Estimation Results of the number of Electricity Customers Model by
Customer Groups
Customer Group
MEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Central PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Northeastern PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Northern PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Constant
1,976,452
1,614,032
327,668
17,590
697.1429
1,580.2860
Ti
68,920
51,100
17,564
274.75
99.8571
56.9286
adj.R2
0.9957
0.9913
0.9505
0.9044
0.9541
0.9468
7,268,434
6,796,931
369,634
20,964.33
1,162.7330
1,175.1970
51,150
1,191.0303
39,361
1,327,497
1,187,135
112,574
9,913.7330
812.9333
798.7576
8,965.6061
116.0455
13,668
2,694,772
2,568,563
97,723
3,145
115.4000
116.5455
18,587
487.0455
8,966.9167
2,047,445
1,943,420
77,769
3,669.200
71.6000
252.9674
13,558
556.6212
8,840.8889
438,270
402,298
27,361
1,413.857
223.0286
158.3287
4,129.7552
172.1364
5,380.2889
100,641
92,283
6,150.2797
788.6000
143.5429
62.5245
825.0350
21.2622
1,201.3556
143,637
131,869
9,281.2483
185
22.6000
22.4930
1,313.7937
69.8007
1,489.1333
100,598
90,737
7,974.8322
236.0857
22.8857
36.1522
1,194.0909
66.0455
1,160.4444
0.9901
0.9894
0.9944
0.9979
0.9399
0.9668
0.9572
0.9729
0.8886
0.9900
0.9900
0.9848
0.9943
0.9137
0.9551
0.9445
0.8048
0.8069
0.9866
0.9862
0.9882
0.9937
0.9690
0.9661
0.9653
0.9672
0.8764
0.9769
0.9715
0.9967
0.9981
0.9626
0.9266
0.9402
0.9886
0.8488
Organization
Organization
Organization
Organization
Organization
106
Table 7.2
(Continued)
Customer Group
Southern PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit Organization
Agricultural Pumping
Temporary
NB series starts at j = 7 (1998)
Constant
1,198,720
1,097,813
81,568
4,236.4000
162.8000
362.1818
10,039
31.3182
7885.3611
Ti
93,395
87,409
3,954.6818
204.1914
34.2000
52.3566
769.8357
15.0280
1529.3556
adj.R2
0.9992
0.9992
0.9861
0.9961
0.9623
0.9427
0.9736
0.6133
0.9135
7.6 Average Electricity Price Model
Data on the average electricity prices are annual data between 1992 and 2003.
The average electricity prices will be forecasted by a simple linear time trend
PRICEijr = CON + Pi *j
(7.25)
where PRICEijr is the average electricity price of the i th group customers in the r
system in year j (j=1 for 1992, 2 for 1993…)
CON = constant
Pi = rate of annual price increase of the i customer group(baht/kwh)
Estimation results of the model are presented in Table 7.3
Table 7.3
Estimation Results of the Average Electricity Price Model
Customer Group
MEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit Organization
PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit Organization
Agricultural Pumping
Temporary
Constant
1.5601
1.7396
2.0464
1.4569
1.2774
1.4568
1.4262
1.4096
1.2287
1.9545
1.4076
1.2602
1.6004
1.4109
Pi
0.0953
0.0963
0.0907
0.1071
0.0958
0.0861
0.0929
0.0867
0.1094
0.0877
0.1045
0.0832
0.0752
0.0930
adj.R2
0.9512
0.9652
0.9664
0.9614
0.9638
0.9229
0.9538
0.9494
0.9693
0.9652
0.9543
0.9512
0.9104
0.9579
1.9340
0.1955
0.7204
107
Table 7.3
(Continued)
Customer Group
Central PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Northeastern PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Northern PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Southern PEA
Residential
Small General Service
Medium General Service
Large General Service
Specific General Service
Government and Non–Profit
Agricultural Pumping
Temporary
Organization
Organization
Organization
Organization
Constant
Pi
adj.R2
1.4160
2.2028
1.4126
1.2609
1.6716
1.4301
0.9321
1.8570
0.1163
0.0921
0.1124
0.0895
0.0747
0.0991
0.1061
0.2253
0.9789
0.9679
0.9584
0.9660
0.8951
0.9616
0.9635
0.7565
1.1024
1.8945
1.4690
1.3949
1.7384
1.4258
0.9146
1.9859
0.1179
0.0961
0.1125
0.0910
0.0720
0.1017
0.1070
0.2173
0.9704
0.9669
0.9577
0.9598
0.8896
0.9666
0.9633
0.7680
1.1935
1.9468
1.4965
1.3913
1.6821
1.4269
0.9083
1.7911
0.1166
0.0951
0.1084
0.0808
0.0760
0.0997
0.1076
0.2201
0.9707
0.9732
0.9581
0.9241
0.8904
0.9591
0.9661
0.6365
1.2657
1.9741
1.3941
1.3211
1.6716
1.4206
0.9266
2.2925
0.1184
0.0950
0.1148
0.0880
0.0747
0.1012
0.1078
0.1958
0.9748
0.9745
0.9575
0.9558
0.8951
0.9658
0.9525
0.7857