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

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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