Welcome back to Practical Time Series
Analysis, and welcome to Week 4. We've a lot coming up this week. In particular, we'll be looking at
the partial auto-correlation function. This is an interesting thing, and
it speaks to a pretty fundamental issue. Sometimes we'd like to know the
correlation between two random variables, maybe their measurements. We'd like to measure your thigh
circumference and your arm circumference. If we start taking more and
more measurements about you, you can imagine that these measurements
would all be related to each other. And it's really hard to determine how
two variables are related to each other in a more fundamental way. So we get to the idea of telling us
something new, tell me something new. Okay, we figure out how two
random variables are correlated after we control for the effects of other
random variables that are in the model. The PACF is a wonderful concept, and
we'll deal with it in detail this week. We'll also revisit the Yule-Walker
equations, not just as interesting and elegant mathematical constructs, but
as ways to help us do estimation. If you think about it, a time series
that you find in nature might be an AR, might be an MA, who knows what it is. It's not as often as you
might think that we'll have deep fundamental knowledge of
the factors generating a time series. So estimation is an art,
it's not something to be treated lightly. You need to figure out what
the orders involved are, as well as the actual coefficients. And Yule-Walker will help us there. We'll also take time this week and study
several practical real world examples and some real-world datasets. Have a terrific week.