First of all, sorry to *Gerard.
*I have changed my email account, and I don't know how to reply to my posted
thread before. So I just create a new message here.
Thanks again for your help! Now I realized where my mistake is.
I forgot to include the seasonal differencing order.

After I corrected the formula as below:
(*S-ARIMA(p,d,q)*(P,D,Q)* models, where *p=1,d=0,q=1; P=0,D=1,Q=1;* and *the
seasonal period S=45*.)

X(t) = X(t-45) + ar1*X(t-1) - ar1*X(t-46) - ma1*a(t-1) - sma1*a(t-45) +
ma1*sma1*a(t-46) + a(t)

Thus, we get:

a(t) = X(t) - ar1*X(t-1) - X(t-45) + ar1*X(t-46) + ma1*a(t-1) + sma1*a(t-45)
- ma1*sma1*a(t-46),
*when t>=46*;

Now my question is that: *What is the initial value of a(t) when t<46?
*And what is the initial setting in R?

Because R gives a very good forcasting of the analyzed data series, and I
just can not reproduced the results in other software  (like EXCEL).

Hope some one to help! Thanks!

saji from Shanghai

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