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So in this lecture, we will look at another example of how to use Varma in Python.

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This time we're going to use a data set that is a bit more complicated to work with.

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This data set falls into the field of econometrics, which is probably the most common application of

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vector auto regression in this case.

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The prevailing wisdom tells us that there should be some temporal correlation between different time

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series.

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So again, we'll start by updating stats models and then putting the same libraries we did before.

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The next step is to download the data now, one kind of interesting thing about this data set is that

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it's pretty common to see in classes on econometrics, but for some reason, statisticians never split

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their data into train and test and never evaluate their models on out of sample data.

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So they tend to generate forecasts in the future, which you cannot even check with the Give and Time

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series.

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I'm not sure why this is, but that tends to be how statisticians do things for us.

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We will check our forecasts and get a true sense of how accurate our predictions really are.

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OK, so the next step is to read in our data file using to read Excel.

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Note that this is an Excel spreadsheet, not a ESV.

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The next step is to call the FDA ahead to see what our data looks like.

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OK, so we've got a bunch of time series, but it's not clear what anything is since this is not a class

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about economics.

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We're not going to really worry too much about the meaning behind this data.

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But you're encouraged to study economics on your own if that's what interests you.

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It really is a different topic.

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So it won't be of much use.

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At the same time, if you've taken my finance course, you should have some intuition for the data will

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be using.

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So that's helpful, but not necessary.

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Also, notice that the date is not in a format we typically use.

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In this case.

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We have the year followed by the quarter with a colon in between.

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Note that the second number is not in months.

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It goes one, two, three, four and then back to one.

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So these are quarter's.

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The next step is to write a function to pass the date column as before, the goal is to use the appli

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function, which will map this function onto each row.

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So inside the function, we're going to start by splitting the data by the colon.

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So this gives us the year in the quarter as strings.

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Now, what we would like to do is convert the quarter into a month.

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I encourage you to go through this equation on your own.

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But basically we want a function that will map one to January two to April three to July and four to

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October.

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So one goes to one, two goes to four, three goes to seven and four goes to ten.

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In other words, it's a linear equation.

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The intuition here is that the output should go up by three and the offset is one since January is encoded

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as one.

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OK, so this equation will give us the month.

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The next step is to put this into a string along with the year.

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The final step is to convert this into a daytime object using the strip time function.

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The next step is to call appli passing in the function we just made.

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The next step is to call DFG head again to see that our new column has been created successfully.

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OK, so you can see that we now have a dead column where the months go up by three as expected.

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The next step is to set the date column as the index for the data frame will also drop these unnecessary

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columns.

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We don't need any more.

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The next step is to set the frequency of our index, which is in quarter's.

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The next step is to call the FDA had again to check the format of our data frame.

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So you can see now that the old columns are gone and we have a new date index.

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OK, so the next step is to look at our data for this example, we'll be looking at GDP and something

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called the term spread.

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I'll explain what term spread means very shortly.

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But GDP stands for gross domestic product.

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The technical definition is that it's the total market value of the goods and services produced within

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a country within a specific time period.

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In this case, three months.

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Basically, it's a measure of a country's economic health.

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So this column is stored as GDP C ninety six.

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OK, so notice that this column has a very strong trend, in other words, it's non stationary.

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So using what we learned about Arima, we know that we should difference this column before applying

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any kind of model.

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In practice, we're going to take the log difference, which is the same thing we do with stock prices.

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So this should be unsurprising.

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We'll call this GDP growth.

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The next step is to compute the term spread.

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Now, this one is a bit more complex.

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To understand this, you should be familiar with fixed rate investments like Treasury bills or whatever

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they have in your country.

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So if you go to your bank's website and look up fixed rate investments you can buy, that would be the

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equivalent of this.

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OK, so what is spread?

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The spread is the difference between a long term investment and a short term investment.

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In this case, a 10 year investment and the three month investment.

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So, again, if you go to your bank's website and look up the fixed rate investments, you should notice

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this pattern.

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The pattern is that short term investments usually have lower interest rates than long term investments.

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This makes sense because you should be rewarded for giving up your money for longer periods of time.

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Now, the difference between these two rates fluctuates over time.

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So sometimes you'll see that the long term investment offers a much higher rate, but sometimes you'll

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see that they are nearly the same.

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Now, again, I don't want to get into economics, but this is important for people who care about things

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like interest rates for us.

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The interesting part is that these two time series may be related.

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The next step will be to plot the term spread.

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OK, so notice that it's not quite stationary, but there isn't any upward or downward trend, so we

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might be justified in leaving this as is notice that there seems to be some cyclical pattern, although

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it's not as strong as something like a sine wave.

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So at this point, since we now have a good understanding of this data and we've seen what it looks

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like, this is a good time to stop in the next lecture.

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We'll continue with the usual steps of fitting the model, making the forecast and so forth.