OK, so in this lecture, we are going to continue looking at our Gaja notebook.
The next step is to consider a full Gargash model, specifically the guards one one.
This happens to be the most popular Gargash due to the fact that it fits Financial Times series quite
well, while also being very simple.
As you recall, statisticians tend to prefer parsimonious models.
So we'll start by calling the arch model function, specifying the model type as gargash and setting
both incudes.
One note that the last three arguments are not really necessary, since currently these are the default
values.
The next step is to call a function.
The next step is to call the summary function.
OK, so notice a few things.
Firstly, notice that the log likelihood and the AIC are much better than before.
This is a sign that this model is a much better fit.
The next thing to notice is that the Beetle one coefficient has a very small P value indicating that
it is very significant.
This makes sense given the improvement in the likelihood.
The next step is to store the conditional volatility in the data data frame under the column name Gaja
one one, we'll also plot this against the one and against the original scaled time series.
OK, so this may be a bit hard to see, but basically you can tell that the model is able to match the
higher values as well as the lower values.
The next step is to make a forecast using the same start date as before, as you recall, we chose this
start date because the value was very high on this date.
So we expect to see the forecasts converge downwards.
The next step is to store the variance forecast using essentially the same code as before.
The next step is to compute the absolute value of the scale time series.
Note that the Time series itself is on the same scale as the volatility, while the Square of the Time
series is on the same scale as the variance.
So either of these is fine, but you just have to pick which one you want to use.
The next step is to plot the scale time series with the one forecast and the large one one forecast.
So there are two things you should notice about this.
Firstly, notice that the garden model matches the actual data much more closely.
The arch one seems to not be able to reach those high values.
Secondly, notice how quickly the arch one converges compared to the Ghazwan one.
That is to say, the arch model is much more persistent.
So, as you recall, one possible option when we create the garbage is what kind of distribution to
use by default.
This is the normal, but we've heard that the student t distribution may be a better fit for financial
returns.
So the next step is to create another Ghazwan one, but this time using the T distribution instead of
the default.
As before, the next step is to call modeled that fit.
And again, we're going to look at the model summary.
So as you can see, the log likelihood has again improved, as has the AC.
Notice also that all of the search parameters are still significant.
And also notice that there is one more parameter under distribution since, as you recall, the T distribution
has a parameter called NU, which is the degrees of freedom.
This also has a significant P value.
OK, so the next step is, again, to store the condition of volatility and to plot the results, this
time we're going to plot the Garden one Wante against the March one, one normal.
OK, so you can see that the results look essentially the same, although you may be able to see the
differences more clearly if you zoom in.
The next step is to compute the forecast.
The next step is to store the forecast for the same dates as before.
The next step is to plot the forecasts for both Gargash models we've created.
So what we can see from this is that the new model seems to reach an even higher value and it seems
to have even more persistence than the one one normal.