[R-SIG-Finance] Forecasting a ARMA(1,1)/GARCH(1,1) model

[gustavo99]

Hi, i am working in the forecast   of the daily  price crude .
The last prices of this data are the following:
 100.60 101.47 100.20 100.06  98.68 101.28 101.05 102.13 101.70  98.27
  101.00 100.50 100.03 102.23 102.68 103.32 102.67 102.23 102.14 101.25
  101.11  99.90  98.53  96.76  96.12  96.54  96.30  95.92  95.92  93.45
  93.71  96.42  93.99  93.76  95.24  95.63  95.95  95.83  95.65  96.61
  91.30  91.66  96.23  94.44  94.50  96.52  97.07  97.37  95.31  96.10
  94.35  93.34  93.68  93.65  95.16  94.32  94.82  94.93  95.72  96.41 
  96.70  95.87  95.46  96.83  96.49  96.70  99.61 100.84  99.90  99.65
  99.22  98.84  99.08  97.53  98.51  99.17 100.07 101.49 102.40 103.24
102.36 100.70 100.93 104.43 105.67 106.23 109.98 108.80 109.10 108.86 108.68
109.59 110.41
The data consist of 2973 observations.

For the analisys i considered the returns, the last ones are:
0.0066998270  0.0090753250  0.0141900670  0.0089664010  0.0082031250
-0.0085238280 -0.0162172720  0.0022840120  0.0346774990  0.0118739830
  0.0052995170  0.0353007620 -0.0107292230  0.0027573530 -0.0021998170
 -0.0016535000  0.0083732060  0.0074824350

For modelling the mean i fit an ARMA(1,1) and fot the volatility i fit a
GARCH(1,1) , i used a t-student as conditional distribution, for this i used
the fGarch librray, the code is the following:

h<-garchFit(~arma(1,1)+garch(2,2),data=R,cond.dist="std",TRACE=F)

On the other hand, for the prediction i use the function "predict".
predict(h,10)
   meanForecast  meanError standardDeviation
1   0.001451401 0.01531682        0.01531682
2   0.001265062 0.01540083        0.01539350
3   0.001263344 0.01549628        0.01548892
4   0.001263328 0.01557306        0.01556565
5   0.001263328 0.01566420        0.01565676
6   0.001263328 0.01574062        0.01573312
7   0.001263328 0.01582800        0.01582047
8   0.001263328 0.01590372        0.01589614
9   0.001263328 0.01598779        0.01598018
10  0.001263328 0.01606258        0.01605493

I am modelling this Y_t-mean=e_t=sigma_t*Z_t
however, my question is ,the prediction for the return itself  is the mean
forecast?
if this is the case my prediction for the price would be   equal to
(1+.001451401)*110.41 =110.57
but i think this is not a good prediction, because   the volatility is not
affecting so much  , in addition the predicted prices are growing up
nevertheless i would expect that at some point these ones decrease .

So i would expect that the prediction for the return would be different. but
i certanly dont know which is.

I would apreciate if you could help with this.

Greeting
Gustavo








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