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Model
|
|---|
|
ARMA (1, 1)
|
\( \widehat{b} \)
|
S.E. (\( \widehat{b} \))
|
p value
|
RMSE
|
|
Constant
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5.90
|
1.67
|
0.001*
|
8.68
|
|
AR (1)
|
0.66
|
0.13
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< 0.001*
|
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MA (1)
|
−0.37
|
0.16
|
0.025*
|
|
Modified Box-Pierce test
|
Lag
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Chi-square
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df
|
p value
|
|
12
|
24.0
|
9
|
0.004*
|
|
24
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33.9
|
21
|
0.037*
|
|
ARMA(1, 2)
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\( \widehat{b} \)
|
S.E. (\( \hat{b} \))
|
p value
|
RMSE
|
|
Constant
|
0.72
|
0.07
|
< 0.001*
|
10.06
|
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AR (1)
|
0.96
|
0.25
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< 0.001*
|
|
MA(1)
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0.25
|
0.29
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0.384
|
|
MA (2)
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0.71
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0.20
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0.001*
|
|
Modified Box-Pierce test
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Lag
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Chi-square
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df
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p value
|
|
12
|
40.7
|
8
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< 0.001*
|
|
24
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80.7
|
20
|
< 0.001*
|
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ARMA (1, 1) × (0, 1)12
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\( \hat{b} \)
|
S.E. (\( \widehat{b} \))
|
p value
|
RMSE
|
|
Constant
|
6.42
|
2.21
|
0.006*
|
8.09
|
|
AR (1)
|
0.63
|
0.14
|
< 0.001*
|
|
MA (1)
|
−0.38
|
0.16
|
0.026*
|
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SMA (1)
|
−0.41
|
0.14
|
0.005*
|
|
Modified Box-Pierce test
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Lag
|
Chi-square
|
df
|
p value
|
|
12
|
13.2
|
8
|
0.104
|
|
24
|
19.9
|
20
|
0.466
|
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ARMA auto-regressive moving average, ARMA (p, q) × (P, Q)
h
mixed seasonal ARMA, \( \widehat{\boldsymbol{b}} \) coefficient, df degree of freedom, S.E. (
\( \widehat{\boldsymbol{b}} \)
) standard error of coefficient, RMSE root mean square error
- *p value <0.05 is significant