Temperature correction of energy consumption time series

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Temperature correction of energy consumption time series

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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

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

- But temperatures do not exhibit perfect seasonality

- 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

- 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

- 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

- 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

- Why won’t the following work?

- So we use this:

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

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

- 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

- 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!

- 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

- 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