預測國內能源電力消費

Forecast For Domestic Electric Power Expenses

作者：

系級：

學號：

D9765656 D9765660 D9765554 D9765906 D9765851

開課老師：

課程名稱：

開課系所：

開課學年： 99 學年度 第 二 學期

AREMOS

1990

1

2010

12

252

12

ARIMA

MSE MAD MPE MAPE

Abstract

Abstract

Abstract

Abstract

In order to better understand electric power expenses in Taiwan, we study “the

domestic energy use - electric power” which was obtained from the AREMOS

economic statistics information database. The time period is from January 1990 to

December 2010, total 252 observations. We save the last 12 observations for

out-of-sample forecasts. We apply four kinds of statistical methods/models for

forecasting, which included the time series regression,

exponential smoothing

,

decomposition method

, and the ARIMA model to model this time series. In order to

evaluate the forecast performance, we employ MSE, MAD, MPE, and MAPE four

criteria to evaluate the performance of the four methods. Based on MAPE criterion,

we found that the

decomposition method with X11 and regression technique has the

best performance (about 2.3%) among the four methods which

is able to effectively

forecast domestic electric power to expend in Taiwan for the future .

Keywords

ARIMA; Electric power expense; out-of-sample forecast;

Decomposition Method; X11, Exponential Smoothing.

5

8

9

13

13

15

15

(Time Series Regression)

16

(Decomposition Method)

20

(Exponential Smoothing)

24

ARIMA

25

30

32

33

2-1.1

9

3-1.1

15

3-2.1

log

16

3-2.2

17

3-2.3

95%

(

) 19

3-3.1

20

3-3.2

20

3-3.3

21

3-3.4

21

3-3.5

21

3-3.6

22

3-3.7

95%

23

3-4.1

24

3-4.2

95%

95%

25

3-5.1

25

3-5.2

log

26

3-5.3

26

3-5.4

ACF

PACF

27

3-5.5

ACF

PACF

27

3-5.6

ACF

PACF

28

3-5.7

29

3-5.8ARIMA

95%

(2010

)

30

1-1.1

99

7

2-3.1 MAPE

14

3-4.1

(

)

24

3-5.1 ARIMA

29

3-6.1

31

235

238

...

(

)

1

(

)

0.62

2007

2

24

(2008)

28

C

9.6

60W

11W

36.8

13.5

POLO

(2008)

1-1(

99

)

AREMOS

1990

1

2010

12

252

12

ARIMA

MSE MAD

MPE MAPE

2-1.1

(

)

AREMOS

Excel

(

)

(KLOE)

1990

1

2010

12

252

252

240

12

2010

1

2010

12

ARIMA

2010

ARIMA

MSE MAD MPE

MAPE

2-1.1

/

ARIMA

2010

(

)

1.

(Trend

TR )

_t

(Season

SN )

t

(

ε

t

)

t t t t

TR

SN

y

=

+

+

ε

2.

(Decomposition Method)

(Trend;

TR )

_t

(Season;

SN )

t

(Cyclical;

CL )

t

(Irregular;

IR )

_t

(

y )

t t

y =f(

TR ,

t

SN ,

t

CL ,

t

IR )

t

X11

t

y =

TR +

t

SN +

t

CL +

t

IR

t t

y =

TR

t

×

SN

t

×

CL

t

×

IR

t

3.

Exponential Smoothing

Winters Method‐Additive

Winters

Method‐Multiplicative

Damped Trend

Winters Method‐Additive

m s t tm t m t s t t t t t t t t t t s t t t

S

b

L

F

S

L

Y

S

b

L

L

b

b

L

S

Y

L

+ − + − − − − − − −

+

=

−

+

−

=

−

+

−

=

+

−

+

−

=

)

(

)

1

(

)

(

)

1

(

)

(

)

)(

1

(

)

(

1 1 1 1 1

δ

δ

γ

γ

α

α

Winters Method‐Multiplicative

m s t tm t m t s t t t t t t t t t t s t t t

S

b

L

F

S

L

Y

S

b

L

L

b

b

L

S

Y

L

+ − + − − − − − − −

+

=

−

+

=

−

+

−

=

+

−

+

=

)

(

)

1

(

)

/

(

)

1

(

)

(

)

)(

1

(

)

/

(

1 1 1 1 1

δ

δ

γ

γ

α

α

Damped Trend Exponential Smoothing

1 1 1 1

)

1

(

)

(

)

)(

1

(

− − − −

Φ

−

+

−

=

Φ

+

−

+

=

t t t t t t t t

b

L

L

b

b

L

Y

L

γ

γ

α

α

4.

ARIMA

ARIMA

Box-Jenkins

.

ARIMA

3

(1)

(

AR

) (2)

(

MA

) (3)

(

ARIMA

) ARIMA

ARIMA

(1)

ARIMA

(2)

(3)

(4)

AR(P)

Z

t

=

φ

1

Z

t−1

+

φ

2

Z

t−2

+

...

+

φ

p

Z

t−p

+

a

t

MA(q)

Z

t

=

a

t

−

θ

1

a

t−1

−

θ

2

a

t−2

−

...

−

θ

q

a

t−q

ARMA(p,q)

q t q t t t p t p t t t

Z

Z

Z

a

a

a

a

Z

=

φ

_{1 −1}

+

φ

_{2 −2}

+

...

+

φ

₋

+

−

θ

_{1 −1}

−

θ

_{2 −2}

−

...

−

θ

₋

:

1.

(White noise test)

,

,

H0

H1

P‐value >0.05

H0

P‐value<0.05

H0

H0

P‐value >0.05

2.

(Unit Root Test)

H0

(

)

H1

(

)

P‐value>0.05

H0

P‐value < 0.05

H0

H0

P‐value <0.05

3.

(1)

(2)

(3)

DW

*

:

Pr<DW

=0.05

Pr>DW

=0.05

12

n

y

t

i

yˆ

t

t

(

)

2 1

ˆ

1

∑

=

−

n t t t

y

y

n

%

100

ˆ

1

1

×













₋

∑

= n t t t t

y

y

y

n

%

100

ˆ

1

1

×

−

∑

= n t t t t

y

y

y

n

1.

(Mean Absolute Deviation, MAD)

0

MAD =

∑

=

−

n t t t

y

y

n

1

ˆ

1

2.

(Mean Squared Error, MSE)

MSE = RMSE= MSE

3.

(Mean Percentage Error, MPE)

MPE =

4.

(Mean Absolute Percentage Error, MAPE)

MAPE =

MAPE

:

MAPE(%)

評估

<5

高準確的預測

6-10

尚可的預測

>10

不準確的預測

2-3.1 MAPE

ARIMA

2010

MSE MAD MPE

MAPE

3-1.1

3-1.1

2008

2009

3-1.1

7

9

12

2

3-1.1

2008

9

2008

2009

1

3-2.1 log

3-1.1

log

3-2.1

log

DW

Pr<DW

0.05

t t

M

M

M

M

M

M

M

M

M

M

M

t

y

ε

+

+

+

+

+

+

+

+

−

−

−

−

+

=

∗ 11 10 9 8 7 6 5 4 3 2 1

0658

.

0

1327

.

0

1853

.

0

2015

.

0

1533

.

0

0112

.

0

0699

.

0

00722

.

0

0146

.

0

01232

.

0

0305

.

0

004557

.

0

3744

.

14

)

log(

* t t

y

y

=

t t t t t

=

0

.

358025

ε

−1

+

0

.

291779

ε

−2

+

0

.

275252

ε

−3

+

a

ε

)

,

(

~

2 . . .

σ

µ

N

a

d i i t

σ

ˆ

=

0

.

003742

Mt

12

12

95%

:

3-2.2

3-2.2

95%

2009

1

:

1.2008

7

9

2.2008

7

3.2008

9

2009

1

2008

9

2008

9

(

227

)







=

0

₁

if

_if

t

_t

<

_≥

227

₂₂₇

t

s

DW

Pr<DW

=0.05

12

12

95%

:

3-2.3 95%

(Decomposition Method)

3-3.1

3-3.1

3-3.3 3-3.4 3-3.5

3-3.2

3-3.3

3-3.4

3-3.5

DW

Pr<DW

0.05

Pr<DW

Pr>DW

0.05

12

12

95%

:

3-3.6

95%

2008

9

DW

Pr<DW

=0.05

12

12

95%

:

3-3.7 95%

3-4.1

3.4-1

Winters

Method‐Multiplicative

3-4.1

3-4.1

12

12

95%

3500000 4000000 4500000 5000000 5500000 6000000 6500000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

公 秉 油 當 量 公 秉 油 當 量 公 秉 油 當 量 公 秉 油 當 量

月份

月份

月份

月份

ACTUAL

Predicted value for POWER Upper 95% Confidence Limit Lower 95% Confidence Limit

3-4.2 95% 95%

3-3.2

95%

ARIMA

3-5.1

3-5.1

3-5.2 log

3-5.3

3-5.2

3-5.4 ACF PACF

3-5.4

ACF

(

)

lag12

lag24

3-5.5

ACF

MA(q)

ACF

lag1

lag12

(q=(1)(12))

Airline model

3-5.6 ACF PACF

log

ARIMA(0,1,1)(0,1,1)s NOINT

3-5.6

ACF

PACF

3-5.7

3-5.7

(

)

lag

=0.05

H0

lag

=0.05

H0

ARIMA(0,1,1)(0,1,1)s NOINT

3-5.1 ARIMA

3-5.1

P-value

=0.05

ARIMA(0,1,1)(0,1,1)s NOINT

(1‐B)(1‐B

12

_{) log(}

_Yt

_{)= (1－0.68274B)(1－}

0.80104B

12

_)a

t

~

(

,

)

2 . . .

σ

µ

N

a

d i i t

σ

ˆ

=

0

.

00149

12

12

95%

:

3500000 4000000 4500000 5000000 5500000 6000000 6500000

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

公

秉

油

當

量

公

秉

油

當

量

公

秉

油

當

量

公

秉

油

當

量

月份

月份

月份

月份

ACTUAL

Predicted value for POWER Upper 95% Confidence Limit Lower 95% Confidence Limit

3-5.8 ARIMA 95% (2010 )

3-5.8

95%

ARIMA

ARIMA

95%

ARIMA

95%

Root Mean Square Error

RMSE

Mean Percentage Error MPE

Mean Absolute Percentage Error MAPE

Mean Absolute

Deviation MAD)

RMSE MPE MAPE MAD

欄 1

MAD

RMSE

MPE

MAPE

分解法

110906.4167

2.38E+10

0.846

2.2855

指數平滑法

113347.8333

24358458830

0.3266

2.3146

Time Series

120988.0283

22036390046

-0.4955

2.5006

ARIMA

124012.9167

23197502466

-0.4501

2.5524

3-6.1

3-6.1

MAPE

2%~3%

MSE

2008

8-9

2007

1.

2011

2.

3. AREMOS

http://cache.moe.edu.tw/aremos_ly/search.html

4.

http://acqy.csai.cn/user2/51384/archives/2009/41819.html

5.

http://www.peopo.org/sukusan/post/23202

6.

http://www.taipower.com.tw/

7. Bowerman, B., O'Connell, R., and Koehler, A. (2005) Forecasting,

Time Series, and Regression, 4th edition, Duxbury Press.