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OK, so in this lecture, we will continue looking at our garbage notebook.

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The first step is to create our train test split of our log returns.

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We'll use an testicles five hundred for no particular reason.

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In the next block of code, we'll investigate why it's important to scale our returns when using search.

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So we'll begin by calling the arch model function.

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As mentioned to the first argument is the training time series.

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We'll specify that we want our model to be a large one one.

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The next step is to call a model that fit.

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OK, so you can see how this prints out a bunch of stuff, such as the lost function at each iteration

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notice that we end up getting a warning telling us that the scale of why is too small.

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It says parameter estimation works better when this value is between one and 1000.

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The recommended rescaling is 100 times why.

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OK, so the lesson is that for Gaj, we need to scale our time series.

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OK, so the next step is to scale our time series will assign the mean of the training series to be

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M and the standard deviation of our training series to be X.

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The next step is to standardize both the train series and the Test series using M and S.

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As you recall, we subtract and divide by X.

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The next step is to create an arch one.

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So notice that for this, we have to specify that vol is arch, although P equals one is the default.

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This is because the default model for this function is actually gaj.

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The next step is to call March one that fit.

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Notice that I've passed in an argument called Update Freak, which shows you how to modify how often

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this function prints out the locks.

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OK, so notice how the training process has completed successfully, and we no longer get any warnings.

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The next step is to call the summary function on the results.

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So we can see a few important things from this.

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Firstly, notice that the mean model is constant mean, as you recall, this is the default setting.

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Secondly, notice that the distribution is normal.

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This is also one of the default settings.

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Third, notice that the method is maximum likelihood.

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Now, if you don't know what that is, will be going over that in a later lecture.

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But if you do, then this should give you some idea of how this model is trained.

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The next thing to notice is the log likelihood.

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If you recall, the log likelihood for our previous model was much worse when we did not scale the time

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series.

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OK, so the next thing to notice is the mean model.

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The mean model says that the meme is about 0.01 something, but also note that the P value for this

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is quite large.

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Furthermore, notice that the confidence interval also contains both positive and negative values.

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The next thing to look at is the volatility model.

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Notice that the arch library uses the same notation we do.

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So the bias term is called omega and the arch coefficient is called out for one.

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Also notice that both of these have highly significant P values.

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OK, so the next step is to plot our modest predictions of the in simple condition of volatility, since

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you've seen this code before.

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There's nothing more to explain.

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So as you can see, the fit seems to be just OK.

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It seems to underestimate when the values are large and overestimate when the values are small.

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The next step is to explore how to forecast most of this stuff we discussed in the code preparation.

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So this should just be a review.

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The first thing we're going to do is call the forecast function with only the horizon.

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So why don't we do this?

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You see that we get a warning telling us about this argument called the Re index, which we discussed

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in the code preparation.

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The next step is to try setting this index argument to true.

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The next step is to simply print out the return value to see what kind of object it is.

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So we can see that it's an object of type arch model forecast.

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Now, as you recall, this object has attributes including mean variance and so forth.

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So the next step is to try printing out the mean.

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So as you can see, what we get back is a data frame.

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It contains all the dates of our original training time series.

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So it starts at two thousand ten or 105, even though these dates don't have a forecast.

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They are simply set to not a number, by the way.

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A really great exercise while you're watching this lecture is to take what you learned in the previous

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lecture and try to guess what we will see.

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Also, notice that the column names are simply a smaller one, each start oh two and so forth.

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So if we scroll down to the bottom, we see that only the final row has actual numbers, as you recall.

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This is because we didn't specify a value for the start argument.

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So it simply assumes that we only want to forecast from the end of the training series.

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Now, let's think about why all these values are the same.

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Well, as you recall, we're just looking at the mean and the default mean model is just constant.

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The next step is to check the variants.

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So again, we get a full size data frame, even though most of these values are just done a number.

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When we scroll down to the end, we can see that the variance forecast is stored in the final row.

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The next step is to check the residual variance, as mentioned when we use a constant mean or zero,

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meaning this will be the same as the variance.

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So if we scroll down to the bottom, we can see that these values are the same.

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The next step is to call the forecast function again, but this time to set RE index defaults.

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So let's look at the main attribute once again.

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So we can see that now because we only have a forecast for the final date.

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This is the only role that shows up in our data frame.

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The next step is to look at the variants.

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So again, it's the same forecast as before, except that we do not have any rows with not a number

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of values.