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 + 9786.05dm2

or other forms?

B is backshift oprator
 

Thanks a lot