temperature correction of energy consumption time series
DESCRIPTION
Temperature correction of energy consumption time series. Sumit Rahman, Methodology Advisory Service, Office for National Statistics. Final consumption of energy – natural gas. Energy consumption depends strongly on air temperature – so it is seasonal. Average monthly temperatures. - PowerPoint PPT PresentationTRANSCRIPT
Temperature correction of energy consumption time seriesSumit Rahman, Methodology Advisory Service, Office for National Statistics
Final consumption of energy – natural gas
• Energy consumption depends strongly on air temperature – so it is seasonal
Gas consumption
0
20000
40000
60000
80000
100000
120000
Gig
aw
att
ho
urs
Average monthly temperatures
• But temperatures do not exhibit perfect seasonality
deviations in temperature from long-term monthly averages
-4.0
-3.0
-2.0
-1.0
+0.0
+1.0
+2.0
+3.0
+4.0
Ja
n-9
1
Ja
n-9
2
Ja
n-9
3
Ja
n-9
4
Ja
n-9
5
Ja
n-9
6
Ja
n-9
7
Ja
n-9
8
Ja
n-9
9
Ja
n-0
0
Ja
n-0
1
Ja
n-0
2
Ja
n-0
3
Ja
n-0
4
Ja
n-0
5
Ja
n-0
6
Ja
n-0
7
Ja
n-0
8
Ja
n-0
9
Ja
n-1
0
de
via
tio
n (
de
gre
es
Ce
lsiu
s)
Seasonal adjustment in X12-ARIMA
• Y = C + S + I• Series = trend + seasonal + irregular• Use moving averages to estimate trend• Then use moving averages on the S + I for
each month separately to estimate S for each month
• Repeat two more times to settle on estimates for C and S; I is what remains
Seasonal adjustment in X12-ARIMA
• Y = C × S × I
• Common for economic series to be modelled using the multiplicative decomposition, so seasonal effects are factors (e.g. “in January the seasonal effect is to add 15% to the trend value, rather than to add £3.2 million”)
• logY = logC + logS + logI
Temperature correction – coal
• In April 2009 the temperature deviation was 1.8°(celsius)
• The coal correction factor is 2.1% per degree• So we correct the April 2009 consumption
figure by 1.8 × 2.1 = 3.7%• That is, we increase the consumption by
3.7%, because consumption was understated during a warmer than average April
Current method – its effect
Coal consumption
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Jan-
95
Jul-9
5
Jan-
96
Jul-9
6
Jan-
97
Jul-9
7
Jan-
98
Jul-9
8
Jan-
99
Jul-9
9
Jan-
00
Jul-0
0
Jan-
01
Jul-0
1
Jan-
02
Jul-0
2
Jan-
03
Jul-0
3
Jan-
04
Jul-0
4
Jan-
05
Jul-0
5
Jan-
06
Jul-0
6
Jan-
07
Jul-0
7
Jan-
08
Jul-0
8
tho
usa
nd
s o
f to
nn
es
unadjusted seasonally adjusted
Current method – its effect
Coal consumption
0
1000
2000
3000
4000
5000
6000
7000
8000
Jan-
95
Jul-9
5
Jan-
96
Jul-9
6
Jan-
97
Jul-9
7
Jan-
98
Jul-9
8
Jan-
99
Jul-9
9
Jan-
00
Jul-0
0
Jan-
01
Jul-0
1
Jan-
02
Jul-0
2
Jan-
03
Jul-0
3
Jan-
04
Jul-0
4
Jan-
05
Jul-0
5
Jan-
06
Jul-0
6
Jan-
07
Jul-0
7
Jan-
08
Jul-0
8
tho
usa
nd
s o
f to
nn
es
seasonally adjusted
temperature corrected and seasonallyadjusted
Regression in X12-ARIMA
• Use xit as explanatory variables (temperature deviation in month t, which is an i-month)
• 12 variables required
• In any given month, 11 will be zero and the twelfth equal to the temperature deviation
Regression in X12-ARIMA
• Why won’t the following work?
12
1
loglogi
tttitit ISCxY
Regression in X12-ARIMA
• So we use this:
12
1
logi
itit ARIMAxY
Regression in X12-ARIMA
• More formally, in a common notation for ARIMA time series work:
t
iitit
Dd
BB
xYBBBB
)()(
)(log)1()1)(()(
12
12
1
1212
• εt is ‘white noise’: uncorrelated errors with zero mean and identical variances
Regression in X12-ARIMA
• An iterative generalised least squares algorithm fits the model using exact maximum likelihood
• By fitting an ARIMA model the software can fore- and backcast, and we can fit our linear regression and produce (asymptotic) standard errors
Coal – estimated coefficients
-15
-10
-5
0
5
10
15
20
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
coef
fici
ent
(per
cen
tag
e)
Interpreting the coefficients
• For January the coefficient is -0.044• The corrected value for X12 is
• The temperature correction is
• If the temperature deviation in a January is
0.5°, the correction is• We adjust the raw temperature up by 2.2%• Note the signs!
12
1
logi
itit xY
itixe
022.1)5.0044.0( e
Interpreting the coefficients
• If is small then
• So a negative coefficient is interpretable as a temperature correction factor as currently used by DECC
• Remember: a positive deviation leads to an upwards adjustment
itix xe iti 1
itix
Coal – estimated coefficients
-15
-10
-5
0
5
10
15
20
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
coef
fici
ent
(per
cen
tag
e)
Gas – estimated coefficients
0
2
4
6
8
10
12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
co
eff
icie
nt
(pe
rce
nta
ge
)
Smoothing the coefficients for coal
Coefficients for coal
-15
-10
-5
0
5
10
15
20
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
co
eff
icie
nt
(%)
Coefficients for gas
0
2
4
6
8
10
12
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
coef
fici
ent
(%)
Comparing seasonal adjustments
Coal consumption, seasonally adjusted
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
Jan-
95
Jul-9
5
Jan-
96
Jul-9
6
Jan-
97
Jul-9
7
Jan-
98
Jul-9
8
Jan-
99
Jul-9
9
Jan-
00
Jul-0
0
Jan-
01
Jul-0
1
Jan-
02
Jul-0
2
Jan-
03
Jul-0
3
Jan-
04
Jul-0
4
Jan-
05
Jul-0
5
Jan-
06
Jul-0
6
Jan-
07
Jul-0
7
Jan-
08
Jul-0
8
tho
usa
nd
s o
f to
nn
es
proposed new factors
current method of temperature correction
Heating degree days
• The difference between the maximum temperature in a day and some target temperature
• If the temperature in one day is above the target then the degree day measure is zero for that day
• The choice of target temperature is important
Smoothing the coefficients, heating degree days model (Eurostat measure)
Coefficients for coal
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
co
rre
cti
on
fa
cto
r, p
er
un
it d
ev
iati
on
fro
m t
he
a
ve
rag
e d
eg
ree
da
y
Coefficients for gas
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
corr
ecti
on
fac
tor,
per
un
it
dev
iati
on
fro
m t
he
aver
age
deg
ree
day
Effect on coal seasonal adjustment
Coal consumption, seasonally adjusted
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
Jan-
95
Jul-9
5
Jan-
96
Jul-9
6
Jan-
97
Jul-9
7
Jan-
98
Jul-9
8
Jan-
99
Jul-9
9
Jan-
00
Jul-0
0
Jan-
01
Jul-0
1
Jan-
02
Jul-0
2
Jan-
03
Jul-0
3
Jan-
04
Jul-0
4
Jan-
05
Jul-0
5
Jan-
06
Jul-0
6
Jan-
07
Jul-0
7
Jan-
08
Jul-0
8
tho
usa
nd
s o
f to
nn
es
using Eurostat degree days
current method of temperature correction
The difference temperature correction can make!
Primary energy consumption
Million tonnes of oil equivalent
Unadjusted Temperature adjusted
2009 211.1 212.6
2010 217.3 211.3
Annual change +2.9% -0.6%