Dear list members,
I am trying to estimate parameters of the AR(1)-GARCH(1,1) model. I have one
additional dummy variable for the AR(1) part.
First I wanted to do it using garchFit function (everything would be then
estimated in one step) however in the fGarch library I didn't find a way to
include an additional variable.
That would be the formula but, as said, I think it is impossible to add a
variable:
garchFit(formula = ~ arma(1,0) + garch(1,1), data=x, include.mean=TRUE)
For that reason I decided to do everything in 2 steps. First I estimate the
AR parameters using arima function because here I can include additional
variable and then, in the second step, I estimate the GARCH part of the
model on the residuals from the AR model.
So, this is how I define the additional dummy variable:
d<-rep(0,991)
for (i in 850:922)
d[i]<-1;
and now the 2 steps:
step1 = arima(x, order = c(1,0,0), xreg=d, include.mean = TRUE)
step2 = garch (step1$res, order = c(1,1), include.intercept = TRUE)
The argument 'xreg' apparently allows me to include another variable.
At this point I wanted to ask you what do you think about the code. Do you
think everything is reasonable and correct?
Ok. And now to the problem I encountered.
In the 2nd step, the program cannot finish the estimation. This is what it
shows:
***** ESTIMATION WITH ANALYTICAL GRADIENT *****
I INITIAL X(I) D(I)
1 4.747742e-04 1.000e+00
2 5.000000e-02 1.000e+00
3 5.000000e-02 1.000e+00
IT NF F RELDF PRELDF RELDX STPPAR D*STEP
NPRELDF
0 1 -3.241e+03
1 9 -3.241e+03 6.72e-06 1.38e-05 4.7e-05 2.0e+09 4.7e-06
1.37e+04
2 16 -3.242e+03 8.84e-05 1.18e-04 1.3e-01 2.0e+00 1.6e-02
8.77e-02
3 20 -3.244e+03 6.76e-04 5.37e-04 6.9e-01 1.3e+00 2.6e-01
8.00e-03
4 22 -3.244e+03 1.53e-04 1.55e-04 7.5e-02 2.0e+00 5.1e-02
1.84e-01
5 24 -3.245e+03 2.69e-04 3.13e-04 1.2e-01 2.0e+00 1.0e-01
2.31e+01
6 26 -3.246e+03 9.61e-05 1.57e-04 4.6e-02 1.5e+00 4.5e-02
7.85e-04
7 27 -3.246e+03 3.77e-05 7.31e-05 4.2e-02 1.1e+00 4.5e-02
1.39e-04
8 28 -3.246e+03 6.77e-05 3.45e-05 6.1e-03 0.0e+00 7.4e-03
3.45e-05
9 30 -3.248e+03 6.91e-04 3.75e-04 6.4e-02 0.0e+00 8.1e-02
3.75e-04
10 32 -3.249e+03 2.17e-04 2.28e-04 2.4e-02 1.8e+00 3.3e-02
2.46e-03
11 34 -3.250e+03 3.51e-04 3.66e-04 4.5e-02 5.4e-01 6.5e-02
1.39e-03
12 36 -3.252e+03 7.61e-04 5.08e-04 8.1e-02 3.4e-01 1.3e-01
1.53e-03
13 44 -3.253e+03 4.73e-05 9.51e-05 1.1e-06 6.7e+00 1.9e-06
2.37e-01
14 45 -3.253e+03 4.08e-07 5.59e-07 1.1e-06 2.0e+00 1.9e-06
2.79e-01
15 46 -3.253e+03 1.69e-08 2.74e-08 1.1e-06 2.0e+00 1.9e-06
2.82e-01
16 55 -3.258e+03 1.73e-03 8.48e-04 3.5e-02 2.0e+00 6.3e-02
2.81e-01
17 57 -3.261e+03 7.56e-04 6.61e-04 6.8e-03 2.0e+00 1.3e-02
4.25e+01
18 59 -3.268e+03 2.22e-03 1.74e-03 1.3e-02 2.0e+00 2.5e-02
8.22e+03
19 61 -3.270e+03 5.11e-04 5.21e-04 2.6e-03 2.0e+00 5.1e-03
1.78e+06
20 67 -3.270e+03 9.28e-06 1.72e-05 9.4e-08 2.7e+01 1.8e-07
9.25e+02
21 68 -3.270e+03 5.41e-08 7.21e-08 9.3e-08 2.0e+00 1.8e-07
1.51e+03
22 77 -3.272e+03 5.88e-04 1.12e-03 6.1e-03 2.0e+00 1.2e-02
1.51e+03
23 79 -3.276e+03 1.41e-03 1.47e-03 4.9e-03 1.7e+00 1.2e-02
4.05e-02
24 86 -3.276e+03 9.34e-06 9.36e-06 6.1e-09 2.9e+01 1.2e-08
1.11e-01
25 88 -3.276e+03 1.83e-06 1.82e-06 1.2e-09 1.3e+02 2.4e-09
1.51e-01
26 90 -3.276e+03 3.61e-06 3.61e-06 2.4e-09 1.7e+01 4.8e-09
1.50e-01
27 92 -3.276e+03 7.14e-07 7.14e-07 4.8e-10 3.1e+02 9.5e-10
1.49e-01
28 94 -3.276e+03 1.43e-07 1.43e-07 9.7e-11 1.5e+03 1.9e-10
1.49e-01
29 96 -3.276e+03 2.85e-07 2.85e-07 1.9e-10 1.9e+02 3.8e-10
1.48e-01
30 99 -3.276e+03 5.69e-09 5.69e-09 3.9e-12 3.8e+04 7.6e-12
1.48e-01
31 101 -3.276e+03 1.14e-08 1.14e-08 7.7e-12 4.7e+03 1.5e-11
1.48e-01
32 103 -3.276e+03 2.28e-08 2.28e-08 1.5e-11 2.4e+03 3.0e-11
1.48e-01
33 107 -3.276e+03 4.55e-11 4.55e-11 3.1e-14 6.5e-01 6.1e-14
-1.08e-01
34 109 -3.276e+03 9.11e-12 9.10e-12 6.2e-15 6.5e-01 1.2e-14
-1.08e-01
35 111 -3.276e+03 1.82e-11 1.82e-11 1.2e-14 6.5e-01 2.4e-14
-1.08e-01
36 113 -3.276e+03 -3.05e+06 3.64e-12 2.5e-15 6.5e-01 4.9e-15
-1.08e-01
***** FALSE CONVERGENCE *****
FUNCTION -3.276262e+03 RELDX 2.479e-15
FUNC. EVALS 113 GRAD. EVALS 36
PRELDF 3.642e-12 NPRELDF -1.078e-01
I FINAL X(I) D(I) G(I)
1 2.607871e-15 1.000e+00 2.453e+06
2 2.088683e-02 1.000e+00 2.110e+03
3 9.812705e-01 1.000e+00 1.556e+03
Warning message:
In sqrt(pred$e) : NaNs produced
Could anyone explain me what is the problem here and why the estimation
cannot be finished in this case? 'False convergence'....but I don't really
understand what is behind this message.
If anyone knows, please help R-help ;)
Thank you in advance
Greetings
Marcin
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