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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

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#### Presentation Transcript

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

• 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

### 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