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Temperature correction of energy consumption time seriesPowerPoint Presentation

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

Final consumption of energy – natural gas

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

Average monthly temperatures

- But temperatures do not exhibit perfect seasonality

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

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?

Regression in X12-ARIMA

- So we use this:

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-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

- 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 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

- 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)

Effect on coal seasonal adjustment (Eurostat measure)

The difference temperature correction can make! (Eurostat measure)