So in this lecture, we'll be summarizing what we've learned in this section, this section looked at
vector auto, regressive and moving average models, which are useful for a multivariate time series.
These can be used whenever you believe that you have multiple time series which can influence each other.
This is typically assumed to be the case for econometrics applications, which is one aspect of finance.
We saw that the Vamo model itself is a pretty straightforward extension of a simply replacing the Time
series with vectors and the parameters with matrices.
We then looked at several examples of AAMA in code.
We learned that Varma takes a long time to train compared to a rhema.
In addition, there is a possibility of overfitting since Vamo parameters grow quite dramatically with
the number of components.
In the case where we have two time series which are truly independent, Vamo might learn false correlations
due to noise.
So it's always important to test against the baseline and choose what works best.
We also learned that at least in stat's models, we have to do different thing ourselves.
This may be because each component of the TIME series may be integrated to a different order.
However, note that this is not really a scientific observation since other libraries and languages
do have Arima implementations.
So this is only a guess.
But maybe the reason why it's not included in stats models is because the developers believe different
things should be explicit.
Of course, if you find that defensing is necessary, then in order to make a forecast, you'll need
to undo the difference as well.
We didn't discuss how to do that in the section, but we will elsewhere in the course.
The next thing to realize is that it is still possible to get even more advanced when it comes to Arima
and Vector AAMA models, we've covered the basics, but there are still a lot more things you could
do in terms of the math and analyzing the properties of these models.
This happens to require a lot more linear algebra, which I would consider to be beyond the prerequisite
level for this cause.
However, I do want to give you a preview in case these are topics you want to explore on your own.
So one interesting thing that can happen is suppose you have a multivariate time series where each time
series is Iwona.
It's possible that some linear combination of these Time series gives you an I zero.
That is, if you multiply each time series by some set of constants and then add them together, you
will get a time series that is stationary.
In other words, you can get a time series that is stationary without different saying this is called
code integration.
So if you want to extend your knowledge of vector auto regression, then this might be an interesting
topic.
Another possible topic of study is the impulse response.
This tells us how each component of the TIME series would evolve if we were to shock the system with
an input to one or more variables.
In fact, the procedure for how this is done involves converting the model into moving average form.
So now you have some idea about why converting between different model types could be useful.