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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