Temperature correction of energy consumption time series

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# Temperature correction of energy consumption time series - PowerPoint PPT Presentation

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
• Energy consumption depends strongly on air temperature – so it is seasonal
Average monthly temperatures
• 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
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
• 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