
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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