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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 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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