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So in this lecture, we will be looking at a notebook to demonstrate Granger causality.

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Note that the beginning of this notebook is very similar to the previous notebook on econometrics,

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so we won't repeat that analysis.

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Simply recall that we are looking at two quarterly time series The Difference GDP and the term spread.

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Recall that the GDP has a strong trend, which is why we took the difference and the term spread, it

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looks like it might be cyclical.

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So let's go to the part where we actually do the tests.

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Now, at this point, you should be asking the question, what is the direction of the Granger causality?

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We know that we're going to pass in a two time series and we know that we're going to get significant

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P values if one of the time series affects the other.

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But is it the first time series that affects the second or the second time series that affects the first?

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In order to know this, you have to check the documentation, which I've pasted in this notebook.

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The states that the test is for whether or not the second column affects the first.

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So in this case, because we've put term spread after GDP growth, we'll be testing whether or not term

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spread can forecast GDP growth.

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Note that have set the Max Light to 18, which is what we used in the previous notebook.

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OK, so we can see that the coefficients are significant at a threshold of five percent for like one.

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For like two, they are again, a significant.

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For like three, they are again significant.

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For like four, they are again, a significant.

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Note that this pattern keeps repeating, but only up to a point at the later legs, you'll see that

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the P values do not pass this five percent threshold.

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Now, let's do the Granger causality test again, but this time let's reverse the order of the columns.

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So now we are testing whether GDP growth can forecast term spread.

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So this time, note that we see very significant P values for all legs, these p values are much smaller

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than the first Test.

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So you might be wondering how can this be?

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How is it possible that if one variable causes the second, that the second can also cause the first?

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This might seem like a paradox, but only if you mistakenly think that this is a test for causality.

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Remember that Granger causality is not actually a test of causality, but a test of forecasting ability.

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This simply means that these are useful input features for making a forecast.