Time Variation of Parameters Used in Electricity Demand Models
Keita Honjo
ResearcherCenter for Environmental Science in Saitama (CESS)
Global Warming Countermeasures GroupAbstract
Many studies estimate the impact of temperature rise on electricity demand based on static regression models (SRMs). However, theassumption of constant parameters is too restrictive to explain electricity demand data containing complex temporal patterns. This study
develops a dynamic linear model (DLM) of monthly electricity demand in Japan and demonstrates that the coefficients of cooling andheating degree days (CDD and HDD) stochastically change with time. The estimation result indicates that electricity use for cooling isdecreasing while electricity use for heating is increasing.

IntroductionData➢ Industrial and residential electricity demands in Japan (Figure 1)⚫ The data source is Electricity Survey Statistics published by Agency
for Natural Resources and Energy.
⚫ The data period is January 1988—March 2016 (N = 339).

The assumption of constant parameters is too restrictive to explainelectricity demand data.
⚫ Time series data of electricity demand contain stochastic trends(Dilaver and Hunt 2011: Energy Economics).
⚫ Price and income elasticities of electricity demand stochasticallychange with time (Arisoy and Ozturk 2014: Energy).

➢ Degree-day indices (CDD and HDD)
⚫ We use the population-weighted means of the degree-day indicesin the central cities of the 47 prefectures.
⚫ The base temperatures of the degree-day indices are determinedthrough the model selection based on AIC.

We develop a dynamic linear model (DLM) of electricity demand inJapan and demonstrate that the coefficients of cooling and heating
degree-days (CDD and HDD) are time varying.

70Model50⚫ The observation equation describes the relationships between electricity
demand and explanatory variables (e.g. CDD, HDD, production, wage, electricity
price, and the earthquake dummy).
⚫ The state equations describe the dynamics of parameters. This study assumes
that parameters follow Gaussian random walk.
⚫ Unknown parameters are estimated by combining the maximum likelihood
estimation and the Kalman filter.
⚫ By the model selection based on AIC, we check whether each parameter is timevarying or not (i.e. the state variance is positive or zero).

40TWhThe DLM consists of an observation equation and state equations.

Observation equation

Industrial

60

30
20

Residential

10

2016/01

2012/01

2008/01

2004/01

2000/01

1996/01

1992/01

1988/01

0

Figure 1: Industrial and residential electricity demands in Japan.

State equations

Figure 2: AIC of the electricity demand models under various
combinations of the base temperatures.

Results⚫ The HDD coefficients showed increasing trends
throughout the period.
⚫ The estimation result indicates that electricity use forcooling is decreasing while electricity use for heating isincreasing.

CDD

0.00150.0005CDD

0.00040.00100.0003HDD

0.0002HDD

0.00050.0001

Figure 3: Time-varying coefficients of the CDD and HDD. The broken lines indicate 95%
confidence intervals.

Acknowledgement
The contents of this poster belong to Honjo, Shiraki, and Ashina (2018) published by PLOS
ONE. KH is financially supported by the Saitama prefecture of Japan.

2014/06

2009/06

2004/06

1999/06

1994/06

1989/06

2014/06

0.00002009/060

2004/06⚫ The CDD coefficients showed increasing trends but
began to decrease in the 2000s.

0.0006

1999/06⚫ In the industrial and residential sectors, the coefficientsof CDD and HDD are time varying (Figure 3).

0.00201994/06⚫ In the residential sector, the base temperatures of CDD
and HDD were estimated at 23°C and 18°C, respectively(Figure 2B).

B) Residential electricity demand

0.0007

1989/06⚫ In the industrial sector, the base temperatures of CDD
and HDD were estimated at 19°C and 11°C, respectively(Figure 2A).

A) Industrial electricity demand