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Welcome back to Practical Time Series
Analysis, and welcome to Week 4.

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We've a lot coming up this week.

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In particular, we'll be looking at
the partial auto-correlation function.

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This is an interesting thing, and
it speaks to a pretty fundamental issue.

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Sometimes we'd like to know the
correlation between two random variables,

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maybe their measurements.

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We'd like to measure your thigh
circumference and your arm circumference.

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If we start taking more and
more measurements about you,

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you can imagine that these measurements
would all be related to each other.

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And it's really hard to determine how
two variables are related to each

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other in a more fundamental way.

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So we get to the idea of telling us
something new, tell me something new.

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Okay, we figure out how two
random variables are correlated

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after we control for the effects of other
random variables that are in the model.

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The PACF is a wonderful concept, and
we'll deal with it in detail this week.

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We'll also revisit the Yule-Walker
equations, not just as interesting and

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elegant mathematical constructs, but
as ways to help us do estimation.

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If you think about it, a time series
that you find in nature might be an AR,

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might be an MA, who knows what it is.

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It's not as often as you
might think that we'll have

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deep fundamental knowledge of
the factors generating a time series.

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So estimation is an art,
it's not something to be treated lightly.

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You need to figure out what
the orders involved are,

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as well as the actual coefficients.

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And Yule-Walker will help us there.

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We'll also take time this week and study
several practical real world examples and

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some real-world datasets.

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Have a terrific week.