OK, so in this lecture, we are going to summarize everything we learned in this section, this section
is in many ways the heart of this course.
When people think about what is Time series analysis, it's often the case that they think of Arima.
You've learned that a rhema can be used for both modeling and prediction.
It can be used to forecast the Time series, but it can also give you very important information about
how that Time series is structured.
The methods you learned in this section tell you directly whether or not a data point depends on past
data points or past errors.
As a side note, do keep in mind that these are linear relationships only.
To be more specific, we started this section by learning about auto regressive models, moving average
models and auto regressive moving average models, which simply combines the previous two.
We learned about each of the and parameters and what they imply about the Time series you're dealing
with.
The next step was to learn about how to choose pre and Q, which interestingly is most intuitive.
When you go backwards from the way they were introduced, starting with D.
D is interesting because it has nothing to do with model parameters, but instead it tells you how many
times your data needs to be different in order to become stationary.
The next step was to learn about how to choose CU using the Akef now, one kind of interesting thing
about the Akef and the pickoff is although they are usually introduced as a pair, one is pretty simple,
while the other is pretty non-trivial.
So don't feel too bad if you don't understand the Sieff on your first try.
Intuitively, we know that the SKW is powerful because it tells us how to choose the number of legs
needed in your auto regressive model.
One important exercise that we completed in the section was to check that the common rules for how to
choose to actually work as promised.
These are not experiments that students would typically do in a time series class.
And I hope that they helped provide you with some intuition for why those rules were.
Now, in modern times, it's often the case that we simply throw computing power at model selection
instead of trying to use heuristics.
So in this section we learned how to use auto arima in order to find the best model.
In order to understand how auto Arima works, we learned about the AIC on the Bisi, which are used
as a score to be optimized when doing model selection.
Once we learn the ins and outs of a and model selection, we apply to what we learned to new data sets,
including champagne sales and stock prices.
The most interesting data, in my opinion, is stock prices.
In fact, what we found was that in essentially all cases, no model was able to beat the Niyi forecast.
This is therefore strong evidence in support of the random hypothesis.
When we looked at the AKF in the pickoff, we found even more evidence to suggest that stock prices
very closely follow a random walk.
Now, this is not to say that the random walk hypothesis is true, but it does imply that trying to
forecast stock movements is nearly as difficult as trying to predict a coin flip.