Temperature correction of energy consumption time series
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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.

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Temperature correction of energy consumption time series

Sumit Rahman, Methodology Advisory Service, Office for National Statistics


Final consumption of energy natural gas
Final consumption of energy – natural gas

  • Energy consumption depends strongly on air temperature – so it is seasonal


Average monthly temperatures
Average monthly temperatures

  • But temperatures do not exhibit perfect seasonality


Seasonal adjustment in x12 arima
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 arima1
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
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




Regression in x12 arima
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 arima1
Regression in X12-ARIMA

  • Why won’t the following work?


Regression in x12 arima2
Regression in X12-ARIMA

  • So we use this:


Regression in x12 arima3
Regression in X12-ARIMA

  • More formally, in a common notation for ARIMA time series work:

  • εt is ‘white noise’: uncorrelated errors with zero mean and identical variances


Regression in x12 arima4
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



Interpreting the coefficients
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!


Interpreting the coefficients1
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






Heating degree days
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





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