Dear all:
I have a question about positive and negative signs of the coefficients of
ARIMA when it is expressed in the equation form. There is the output of
ARIMA(1,1,1)(1,1,1) below:
Function evaluations: 132
Evaluations of gradient: 45
Model 1: ARIMA, using observations 1977:03-1986:12 (T = 118)
Estimated using BHHH method (conditional ML)
Dependent variable: (1-L)(1-Ls) y
coefficient std. error z p-value
---------------------------------------------------------
phi_1 0.0767983 1.75029 0.04388 0.9650
Phi_1 -0.133120 0.159001 -0.8372 0.4025
theta_1 -0.0385106 1.77542 -0.02169 0.9827
Theta_1 -0.662710 0.131924 -5.023 5. 08e-07 ***
The equation should be written in(1-0.0767983B)(1+0.133120B^12)(1-L)(1-L_12)
y_t=(1-0.0385106B)(1-0.662710L^12)a_t
,
(1-0.0767983B)(1+0.133120B^12)(1-L)(1-L_12)
y_t=(1+0.0385106B)(1+0.662710L^12)a_t
or
(1+0.0767983B)(1-0.133120B^12) (1-L)(1-L_12)
y_t=(1-0.0385106L)(1-0.662710L^12)a_t
?B is backshit oprator
which equation is correct?
I don’t know the correct positive and negative signs of the coefficients in the
ARIMA equation.
Another sample is ARIMAX. I add two dummy variables: dm1 is for January, dm2 is
for Febuary. There is the output of ARIMAX(1,1,1) below:
Model 4: ARMAX, 使用中之子樣本範圍: 1997:03-2006:12 (T = 118)
Estimated using BHHH method (最大概似法 conditional ML)
應變數 (Dependent variable): (1-L) new_zwaland coefficient std.
error z p-value
--------------------------------------------------------------
const 6971.19 4629.76 1.506 0.1321
phi_1 -0.0428580 0.174013 -0.2463 0.8055
theta_1 0.719310 0.107846 6.670 2.56e-011 ***
dm1 -78779.9 14357.2 -5.487 4.08e-08 ***
dm2 9786.05 16383.1 0.5973 0.5503
The ARIMAX equation should be written in
(1+0.0.428580B) (1-L)y_t= 6971.19+(1+0.719310B) a_t - 78779.9dm1 + 9786.05dm2,
(1-0.0.428580B) (1-L)y_t= 6971.19+(1+0.719310B) a_t - 78779.9dm1 + 9786.05dm2or
other forms?B is backshift oprator
Thanks a lot
Dear all:
I have a question about positive and negative signs of the coefficients of ARIMA when it is expressed in the equation form. There is the output of ARIMA(1,1,1)(1,1,1) below:
Function evaluations: 132
Evaluations of gradient: 45
Model 1: ARIMA, using observations 1977:03-1986:12 (T = 118)
Estimated using BHHH method (conditional ML)
Dependent variable: (1-L)(1-Ls) y
coefficient std. error z p-value
---------------------------------------------------------
phi_1 0.0767983 1.75029 0.04388 0.9650
Phi_1 -0.133120 0.159001 -0.8372 0.4025
theta_1 -0.0385106 1.77542 -0.02169 0.9827
Theta_1 -0.662710 0.131924 -5.023 5. 08e-07 ***
The equation should be written in (1-0.0767983B)(1+0.133120B^12)(1-L)(1-L_12) y_t=(1-0.0385106B)(1-0.662710L^12)a_t
,
(1-0.0767983B)(1+0.133120B^12)(1-L)(1-L_12) y_t=(1+0.0385106B)(1+0.662710L^12)a_t
or
(1+0.0767983B)(1-0.133120B^12) (1-L)(1-L_12) y_t=(1-0.0385106L)(1-0.662710L^12)a_t
? B is backshit oprator
which equation is correct?
I don¡¦t know the correct positive and negative signs of the coefficients in the ARIMA equation.
Another sample is ARIMAX. I add two dummy variables: dm1 is for January, dm2 is for Febuary.
There is the output of ARIMAX(1,1,1) below:
Model 4: ARMAX, ¨Ï¥Î¤¤¤§¤l¼Ë¥»½d³ò: 1997:03-2006:12 (T = 118)
Estimated using BHHH method (³Ì¤j·§¦üªk conditional ML)
À³ÅÜ¼Æ (Dependent variable): (1-L) new_zwaland
coefficient std. error z p-value
--------------------------------------------------------------
const 6971.19 4629.76 1.506 0.1321
phi_1 -0.0428580 0.174013 -0.2463 0.8055
theta_1 0.719310 0.107846 6.670 2.56e-011 ***
dm1 -78779.9 14357.2 -5.487 4.08e-08 ***
dm2 9786.05 16383.1 0.5973 0.5503
The ARIMAX equation should be written in
(1+0.0.428580B) (1-L)y_t= 6971.19+(1+0.719310B) a_t - 78779.9dm1 + 9786.05dm2 ,
(1-0.0.428580B) (1-L)y_t= 6971.19+(1+0.719310B) a_t - 78779.9dm1 + 9786.05dm2 or other forms? B is backshift oprator
Thanks a lot
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