2011 International Conference on Alternative Energy in Developing Countries and Emerging Economies
- 347 -
TABLE II.
SARIMA M
ODEL
P
ARAMETERS
Estimated Parameters
SARIMA(p, d, q)(P, D, Q)
s
(1, 0, 1)
(3, 1, 1)
8
(1, 0, 1)
(3, 1, 1)
8
no
constant
(1, 0, 1)
(2, 1, 1)
8
no
constant
(1, 0, 1)
(1, 1, 1)
8
no
constant
Constant
Estimate -0.004
-
-
-
p-value
0.567
AR(1):
1
I
Estimate
0.358
0.359
0.368
0.370
p-value
0.000
0.000
0.000
0.000
MA(1):
1
T
Estimate -0.169
-0.168
-0.171
-0.165
p-value
0.023
0.024
0.019
0.024
SAR(1):
1
)
Estimate
0.065
0.066
0.100
0.106
p-value
0.140
0.138
0.019
0.013
SAR(2):
2
)
Estimate -0.071
-0.071
-0.060
-
p-value
0.086
0.087
0.150
SAR(3):
3
)
Estimate -0.122
-0.122
-
-
p-value
0.004
0.004
SMA(1):
1
4
Estimate
0.867
0.866
0.894
0.905
p-value
0.000
0.000
0.000
0.000
TABLE III.
BIC
VALUES AND
L
JUNG
-B
OX
Q
STATISTICS OF
SARIMA(p, d, q)(P, D, Q)
s
SARIMA(p, d, q)(P, D, Q)
s
BIC
Ljung-Box Q (at lag 18)
statistics
p-value
(1, 0, 1)(3, 1, 1)
8
-0.289
16.600
0.165
(1, 0, 1)(3, 1, 1)
8
no constant
-0.299
16.625
0.164
(1, 0, 1)(2, 1, 1)
8
no constant
-0.297
14.838
0.318
(1, 0, 1)(1, 1, 1)
8
no constant
-0.304
16.072
0.309
The second part of this section shows how to construct
model by the decomposition method. From Fig. 3, we
found that wind speed series exhibits constant seasonal
variation, so the additive decomposition model in (2)
should be chosen for this series. Fig. 3 also shows that the
wind speed series do not present the trend component. To
ensure this idea, we have tested the linear trend as shown
in Fig. 8. The p-value of independent variable (Time) is
greater than level of significant 0.05, which means that
the trend component is insignificant, so this component
can be estimated by the average of series. The seasonal
indices from Minitab V.15 for each period display in Fig.
9. Therefore, the forecast additive decomposition model
appear
Period 1: 0.00
O’clock;
t
ˆ
Y
= 3.102785
–
0.144922 = 2.957863
Period 2: 3
.00 O’clock;
t
ˆ
Y
= 3.102785
–
0.342422 = 2.760363
Period 3:
6.00 O’clock;
t
ˆ
Y
= 3.102785
–
0.496172 = 2.606613
Period 4:
9.00 O’clock;
t
ˆ
Y
= 3.102785 + 0.521953 = 3.624738
Period 5:
12.00 O’clock;
t
ˆ
Y
= 3.102785 + 0.856328 = 3.959113
Period 6:
15.00 O’clock;
t
ˆ
Y
= 3.102785 + 0.163828 = 3.266613
Period 7:
18.00 O’clock;
t
ˆ
Y
= 3.102785
–
0.242422 = 2.860363
Period 8:
21.00 O’clock;
t
ˆ
Y
= 3.102785
–
0.316172 = 2.786613.
(6)
Fig. 8. Regression analysis of the wind speed series.
Fig. 9. Seasonal indices of the wind speed series from
the additive decomposition model.
Regression Analysis: ws30m versus Time
The regression equation is
ws30m = 3.20 - 0.000264 Time
Predictor Coef SE Coef T P
Constant 3.20020 0.08299 38.56 0.000
Time -0.0002643 0.0001951 -1.35 0.176
S = 1.12460 R-Sq = 0.2% R-Sq(adj) = 0.1%
Time Series Decomposition for
ws30m
Additive Model
Data ws30m
Length 736
NMissing 0
Seasonal Indices
Period Index
1 -0.144922
2 -0.342422
3 -0.496172
4 0.521953
5 0.856328
6 0.163828
7 -0.242422
8 -0.316172
Fig. 7. Partial autocorrelation function (PACF) of the first seasonal differences, D = 1, of the wind speed data.
