R help - May 2013 - Forecasting MA model different to manually computation?

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

Hello,

Since R is open source, you can look at the source code of package 
forecast to know exactly how it is done. My guess would be

x - m$residuals
Time Series:
Start = 1
End = 3
Frequency = 1
[1] 3.060660 4.387627 3.000000


Hope this helps,

Rui Barradas

Em 22-05-2013 15:13, Neuman Co escreveu:
> 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
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

mh, this is interesting, I would have expected that the following is valid:

If we look at the second value:
4.387627 = 3.5 + (-1)*(5-3.060660) 

or


 4.387627 = 3.5 - (-1)*(5-3.060660) 

but this does not work. Surprise. Nice question!





________________________________
 Von: Neuman Co <neumancohu@gmail.com>
An: r-help@r-project.org 
Gesendet: 16:13 Mittwoch, 22.Mai 2013
Betreff: [R] Forecasting MA model different to manually computation?


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

______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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