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.