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OK, so in this lecture, we are going to summarize everything we learned in this section, this section

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is in many ways the heart of this course.

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When people think about what is Time series analysis, it's often the case that they think of Arima.

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You've learned that a rhema can be used for both modeling and prediction.

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It can be used to forecast the Time series, but it can also give you very important information about

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how that Time series is structured.

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The methods you learned in this section tell you directly whether or not a data point depends on past

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data points or past errors.

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As a side note, do keep in mind that these are linear relationships only.

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To be more specific, we started this section by learning about auto regressive models, moving average

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models and auto regressive moving average models, which simply combines the previous two.

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We learned about each of the and parameters and what they imply about the Time series you're dealing

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with.

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The next step was to learn about how to choose pre and Q, which interestingly is most intuitive.

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When you go backwards from the way they were introduced, starting with D.

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D is interesting because it has nothing to do with model parameters, but instead it tells you how many

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times your data needs to be different in order to become stationary.

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The next step was to learn about how to choose CU using the Akef now, one kind of interesting thing

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about the Akef and the pickoff is although they are usually introduced as a pair, one is pretty simple,

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while the other is pretty non-trivial.

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So don't feel too bad if you don't understand the Sieff on your first try.

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Intuitively, we know that the SKW is powerful because it tells us how to choose the number of legs

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needed in your auto regressive model.

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One important exercise that we completed in the section was to check that the common rules for how to

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choose to actually work as promised.

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These are not experiments that students would typically do in a time series class.

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And I hope that they helped provide you with some intuition for why those rules were.

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Now, in modern times, it's often the case that we simply throw computing power at model selection

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instead of trying to use heuristics.

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So in this section we learned how to use auto arima in order to find the best model.

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In order to understand how auto Arima works, we learned about the AIC on the Bisi, which are used

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as a score to be optimized when doing model selection.

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Once we learn the ins and outs of a and model selection, we apply to what we learned to new data sets,

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including champagne sales and stock prices.

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The most interesting data, in my opinion, is stock prices.

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In fact, what we found was that in essentially all cases, no model was able to beat the Niyi forecast.

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This is therefore strong evidence in support of the random hypothesis.

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When we looked at the AKF in the pickoff, we found even more evidence to suggest that stock prices

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very closely follow a random walk.

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Now, this is not to say that the random walk hypothesis is true, but it does imply that trying to

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forecast stock movements is nearly as difficult as trying to predict a coin flip.