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So in this lecture, we'll be summarizing what we've learned in this section, this section looked at

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vector auto, regressive and moving average models, which are useful for a multivariate time series.

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These can be used whenever you believe that you have multiple time series which can influence each other.

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This is typically assumed to be the case for econometrics applications, which is one aspect of finance.

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We saw that the Vamo model itself is a pretty straightforward extension of a simply replacing the Time

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series with vectors and the parameters with matrices.

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We then looked at several examples of AAMA in code.

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We learned that Varma takes a long time to train compared to a rhema.

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In addition, there is a possibility of overfitting since Vamo parameters grow quite dramatically with

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the number of components.

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In the case where we have two time series which are truly independent, Vamo might learn false correlations

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due to noise.

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So it's always important to test against the baseline and choose what works best.

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We also learned that at least in stat's models, we have to do different thing ourselves.

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This may be because each component of the TIME series may be integrated to a different order.

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However, note that this is not really a scientific observation since other libraries and languages

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do have Arima implementations.

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So this is only a guess.

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But maybe the reason why it's not included in stats models is because the developers believe different

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things should be explicit.

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Of course, if you find that defensing is necessary, then in order to make a forecast, you'll need

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to undo the difference as well.

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We didn't discuss how to do that in the section, but we will elsewhere in the course.

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The next thing to realize is that it is still possible to get even more advanced when it comes to Arima

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and Vector AAMA models, we've covered the basics, but there are still a lot more things you could

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do in terms of the math and analyzing the properties of these models.

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This happens to require a lot more linear algebra, which I would consider to be beyond the prerequisite

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level for this cause.

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However, I do want to give you a preview in case these are topics you want to explore on your own.

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So one interesting thing that can happen is suppose you have a multivariate time series where each time

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series is Iwona.

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It's possible that some linear combination of these Time series gives you an I zero.

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That is, if you multiply each time series by some set of constants and then add them together, you

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will get a time series that is stationary.

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In other words, you can get a time series that is stationary without different saying this is called

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code integration.

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So if you want to extend your knowledge of vector auto regression, then this might be an interesting

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topic.

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Another possible topic of study is the impulse response.

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This tells us how each component of the TIME series would evolve if we were to shock the system with

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an input to one or more variables.

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In fact, the procedure for how this is done involves converting the model into moving average form.

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So now you have some idea about why converting between different model types could be useful.