Temperature correction of energy consumption time series

1. Temperature correction of energy consumption time series Sumit Rahman, Methodology Advisory Service, Office for National Statistics

2. Final consumption of energy – natural gas • Energy consumption depends strongly on air temperature – so it is seasonal

3. Average monthly temperatures • But temperatures do not exhibit perfect seasonality

4. 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

5. 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

6. 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

7. Current method – its effect

8. Current method – its effect

9. 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

10. Regression in X12-ARIMA • Why won’t the following work?

11. Regression in X12-ARIMA • So we use this:

12. 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

13. 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

14. Coal – estimated coefficients

15. 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!

16. 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

17. Coal – estimated coefficients

18. Gas – estimated coefficients

19. Smoothing the coefficients for coal

20. Comparing seasonal adjustments

21. 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

22. Smoothing the coefficients, heating degree days model (Eurostat measure)

23. Effect on coal seasonal adjustment

24. The difference temperature correction can make!