forecasting on daily peak load electricity demand in south ... · increase in electricity demand is...

Forecasting on Daily Peak Load Electricity Demand in South Korea using Seasonal GARCH Models

Sahm Kim Professor, Department of Applied Statistics, Chung-Ang Univ, Korea [email protected]

34th International Symposium on Forecasting

I. Introduction • Demand forecasting has fundamental reasons to be

considered deeply. Effective early warning of an unexpected increase in electricity demand is important to ensure the security of the supply processes in electricity field.

• The blackout on September 15 in 2012 which affected economic and social confusions and losses in Korea is a typical example why the forecasting system based on shot term, such as daily peak data.

• The temperature in Korea has affected the rapid fluctuations of the electricity demand especially in Summer periods.


• Tol (1996) fits a GARCH model to daily Dutch temperature data in winter and summer periods, and demonstrates its usefulness for describing the volatility clustering feature of the data.

• Taylor(2003) showed that the forecasts produced by the double seasonal Holt-Winters method outperform those from traditional Holt-Winters and from a well-specified multiplicative double seasonal ARIMA model.

• Pappas et. al(2008) used the several ARMA models and compared the performance of the models to forcast the electricity demand loads in Greece.


I. Introduction

• Sigauke and Chikobvu(2011) investigated the daily peak electricity demand in South Africa by several time series models such as SARIMA, SARIMA-GARCH and regression SARIMA-GARCH models.

• Kim(2011) used the Seasonal-AR-GARCH model to predict the internet traffic .

• We analyzed the daily peak load data by using several time series models and compared the performance of the models based on the entire and summer period data in South Korea.


I. Introduction

• Seasonal-ARIMA model • ARIMA 𝑝,𝑑, 𝑞 × 𝑃,𝐷,𝑄 𝑠 (Box , Jenkins and Reisel,1994)


II. Time series models

• Modified Holt-Winters model(Taylor, 2003) • The modified Holt-winters models was suggested by Taylor(2003)



• Seasonal-AR-GARCH model • ARCH(Engle, 1982) • GARCH(Bollerslev,1986)

• Seasonal-AR-GARCH is defined by



• Regression-Seasonal-AR-GARCH model • Regression-Seasonal-AR-GARCH



• Original entire data 2003.01.01- 2011.08.11 (number of the daily data : 3145)

• For setting up the model, we used 3089 (2003.01.01-2011.06.17) • For performance evaluation, we used 56 data (2011.06.17-2011.08.11)

• Independent variables : Temperature, Holidays and Sundays

• Holidays : New year’ days(lunar and solar ), Korean Thanks Giving day(lunar) and national holidays.


III. Data Analysis

• Summer data

Summer periods between 2003 and 2011 (number of the daily data : 784) For setting up the model, we used 728 (2003 -2010) For performance evaluation, we used 56 data (2011)


III. Data Analysis


III. Data Analysis • Entire data

max_load

2000

3000

4000

5000

6000

7000

8000

date

2003-01-01 2004-01-01 2005-01-01 2006-01-01 2007-01-01 2008-01-01 2009-01-01 2010-01-01 2011-01-01 2012-01-01 2013-01-01

• Log differenced data(entire)


III. Data Analysis

difload

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

date

2003-01-01 2004-01-01 2005-01-01 2006-01-01 2007-01-01 2008-01-01 2009-01-01 2010-01-01 2011-01-01 2012-01-01 2013-01-01


III. Data Analysis • Summer data

model1

model2

model3

model4

model5

model6


IV. Performance Evaluation

IV. Performance Evaluation Reg Seasonal ARIMA(Entire) Reg Seasonal ARIMA(Summer)


Parameter Estimate Standard Error

Approx Pr > |t|

𝛾𝐻 -0.0993 0.0061 <.0001

𝛾𝑇 0.0101 0.0005 <.0001

𝛾𝑆 -0.1334 0.0309 <.0001

𝜃1 0.9888 0.0071 <.0001

Θ7 0.9174 0.0204 <.0001

Θ91 0.9975 0.0012 <.0001

𝜙1 0.7968 0.0287 <.0001

𝜙3 -0.0772 0.0284 0.0065

Φ7 0.9934 0.0041 <.0001

Φ91 1.0000 0.0000 <.0001

Parameter Estimate Standard error

Approx Pr > |t|

𝛾𝐻 -0.0706 0.0023 <.0001

𝛾𝑇 -0.0010 0.0003 0.0002

𝛾𝑆 -0.0952 0.0137 <.0001

𝜃1 0.0759 0.0180 <.0001

𝜃3 0.6928 0.0349 <.0001

Θ7 0.8171 0.0133 <.0001

Θ364 -0.1525 0.0194 <.0001

𝜙2 -0.1076 0.0180 <.0001

𝜙3 0.4946 0.0403 <.0001

𝜙4 -0.0909 0.0199 <.0001

𝜙5 -0.1177 0.0189 <.0001

Φ7 0.9862 0.0033 <.0001

IV. Performance Evaluation Modified Holt-Winters (Entire)

Parameter Estimate

Level -

Trend 0.1594

Seasonal1 0.1543

Seasonal2 0.2472

Autoregressive 0.8109

Modified Holt-Winters (Summer)

Parameter Estimate

Level 0.3367

Trend -

Seasonal1 0.0229

Seasonal2 0.2425

Autoregressive 0.4963


IV. Performance Evaluation Reg Seasonal-AR-GARCH(Entire) Reg Seasonal-AR-GARCH(Summer)


Variable Estimate Standard Error

Approx Pr > |t|

𝛾𝑇 -0.0026 0.0002 <.0001

𝛾𝑆 -0.0838 0.0030 <.0001

𝛾𝐻 -0.0629 0.0009 <.0001

𝜙2 0.0867 0.0100 <.0001

𝜙3 0.0636 0.0091 <.0001

𝜙5 0.0941 0.0091 <.0001

𝜙6 0.0217 0.0067 0.0012

Φ7 -0.1810 0.0125 <.0001

Φ14 -0.1926 0.0098 <.0001

Φ21 -0.1459 0.0110 <.0001

Φ28 -0.1047 0.0107 <.0001

Φ364 -0.2025 0.0093 <.0001

𝛼0 0.0003 1.03E-05 <.0001

𝛼1 0.5063 0.0291 <.0001

𝛼2 0.3789 0.0210 <.0001

𝛽2 0.0427 0.0111 0.0001

Variable Estimate Standard Error

Approx Pr > |t|

𝛾𝑇 0.0091 0.0005 <.0001

𝛾𝑆 -0.1510 0.0109 <.0001

𝛾𝐻 -0.0807 0.0029 <.0001

𝜙2 0.0495 0.0212 0.0195

Φ7 -0.2321 0.0324 <.0001

Φ14 -0.2364 0.0268 <.0001

Φ21 -0.1108 0.0257 <.0001

Φ91 -0.3243 0.0276 <.0001

𝛼0 0.0002 2.52E-05 <.0001

𝛼1 0.3641 0.0568 <.0001

𝛽1 0.4248 0.0445 <.0001


IV. Performance Evaluation

• Forecast evaluation for the period (2011/06/17~2011/08/11)

model1 model2 Model3 model4 model5 model6

MAPE 4.91 2.61 3.79 3.73 3.90 2.30

• Model 1 : Regression- Seasonal-ARIMA(Entire) • Model 2 : Regression- Seasonal-ARIMA(Summer) • Model 3 : Modified Holt-Winters (Entire) • Model 4 : Modified Holt-Winters (Summer) • Model 5 : Regression- Seasonal-AR-GARCH(Entire) • Model 6 : Regression- Seasonal-AR-GARCH(Summer)

• Regression-Seasonal-AR-GARCH outperforms the other models in terms of the MAPE criterion.

• The forecasting accuracy based on summer periods are better than that which are based on entire years.

• Hourly or shorter data can be applied to the models for more accurate and reliable forecasts.

• More independent variables such as humidity should be considered.


V. Concluding Remarks

forecasting on daily peak load electricity demand in south ... · increase in electricity demand is...

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