[R] AR-GARCH with additional variable - estimation problem

Wed Jul 13 19:24:54 CEST 2011

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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]]
>
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