Problem about SARMA model forcasting
Somebody suggest that all the intial values are zero. So I followed this suggestion and used below formulas to compute the forcast in Excel when t < 46, a(t)=0; when t >= 46, 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); X(predict) = ar1*X(t-1) + X(t-45) - ar1*X(t-46) - ma1*a(t-1) - sma1*a (t-45) + ma1*sma1*a(t-46); But the predict values are not the same as what I got from R software. The time series is non-negative. But there are negative value in what I got from Excel using the above formula. So there must be something wrong. And I just don't where the mistake is. saji from Shanghai
On 2?9?, ??7?54?, Saji Ren <saji.... at gmail.com> wrote:
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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