Marcin P?�ciennik
2011-Jul-13 16:11 UTC
[R] AR-GARCH with additional variable - estimation problem
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
[[alternative HTML version deleted]]
Joshua Ulrich
2011-Jul-13 17:24 UTC
[R] AR-GARCH with additional variable - estimation problem
Please don't cross-post: https://mailman.stat.ethz.ch/pipermail/r-sig-finance/2011q3/008230.html -- Joshua Ulrich ?| ?FOSS Trading: www.fosstrading.com On Wed, Jul 13, 2011 at 11:11 AM, Marcin P??ciennik <pucek8 at gmail.com> wrote:> 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 > > ? ? ? ?[[alternative HTML version deleted]] > > ______________________________________________ > 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. >