# [R] Problem about SARMA model forcasting

saji saji.ren at gmail.com
Wed Feb 11 12:57:14 CET 2009

```Somebody said that ARIMA models like discussed above are easy to
The prediction formula is simply a linear equation that refers to past
values of original time series and past values of the errors.
Thus, setting up an spreadsheet by stroing the data in one column, the
forcasting values computed bu the formula in another column, and the
errors(data minus forcasts) in the third column can give the results
just as the same as any statistical computing software(like R).
But I just can't, and I think there must be some mistakes in my
procedure but just can't find it by myself.
Really need helps!
Thanks again!

saji from Shanghai

On 2月11日, 下午7时54分, saji <saji.... at gmail.com> wrote:
> 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月9日, 下午7时54分, 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
>
> >         [[alternative HTML version deleted]]
>
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