[R] Forecasting MA model different to manually computation?

[Neuman Co]

Hi,
3 down vote favorite
1

I am interested in forecasting a MA model.Therefore I have created a
very simple data set (three variables). I then adapted a MA(1) model
to it. The results are:

x<-c(2,5,3)
m<-arima(x,order=c(0,0,1))

Series: x
ARIMA(0,0,1) with non-zero mean

Coefficients:
          ma1  intercept
      -1.0000     3.5000
s.e.   0.8165     0.3163

sigma^2 estimated as 0.5:  log likelihood=-3.91
AIC=13.82   AICc=-10.18   BIC=11.12

While the MA(1) model looks like this:

X_t=c+a_t+theta*a_{t-1}

and a_t is White Noise.

Now, I look at the fitted values:

library(forecast)
fitted(m)
Time Series:
Start = 1
End = 3
Frequency = 1
[1] 3.060660 4.387627 3.000000

I tried different ways, but I cant find out how the fitted values
(3.060660, 4.387627 and 3.000000) are calculated.

Any help would be very appreciated.



--
Neumann, Conrad