[R] Problem about SARMA model forcasting

Gerard M. Keogh GMKeogh at justice.ie
Tue Feb 3 11:59:58 CET 2009

```Saji,

This may help.

(1,0,1)X(0,1,1)S

giving difference polynomials

nonseasonal (1,0,1) = (1-ar1*B)   =  (1-ma1*B)
seasonal (0,1,1)S   = (1-B**S)    =  (1-sma1*B**S)

giving:  (1-ar1*B)X(1-B**S) x_t = (1-ma1*B)X(1-sma1*B**S) a_t

multiplying out:

x_t - x_(t-S) - ar1*x_(t-1) + ar1*x_(t-S-1) = a_t - ma1*a_(t-1) -
sma1*a_(t-S) + ma1*sma1*a_(t-S-1)

or

x_t =  x_(t-S) + ar1*x_(t-1) - ar1*x_(t-S-1) + a_t - ma1*a_(t-1) -
sma1*a_(t-S) + ma1*sma1*a_(t-S-1)

Hopefully I've multiplied all the bits out correctly and I think R uses
this (Box-Jenkins) form for ARIMA models.

Gerard

刘人润
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Subject
03/02/2009 10:22          forcasting

Hello, Guys:
I'm from China, my English is poor and I'm new to R. The first message I
sent to R help meets some problems, so I send again.
Hope that I can get useful suggestions from you warm-hearted guys.
Thanks.

I builded a multiplicative seasonal ARMA model to a series named
"cDownRange".
And the order is (1,1)*(0,1)45
The regular AR=1; regular MA=1; seasonal AR=0; seasonal MA=1; seasonal
period=45.
I fitted the model in R and get the result as below:
Call:arima(x = cDownRange, order = c(1, 0, 1), seasonal = list(order = c(0,
1, 1), period = 45))
Coefficients:
ar1      ma1     sma1
0.7364  -0.5046  -0.9511
s.e.    0.0458   0.0594   0.0130
When I use the predict command of this model in R, it gives the right
forcasting.

So I think the forcast formula of this SARMA model should be written as
below:
X(t)=ar1*X(t-1)-ma1*a(t-1)-sma1*a(t-45)+ma1*sma1*a(t-46)

But when I use this forcast formula in Excel, it gives a totally different
predict from R. And I don't know why?
I guess the expression of the forcast formula of this SARMA(1,1)*(0,1)45 is
wrong, but I don't know the right form.
Can anybody help me with this?Thank, again!

saji from Shanghai

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