Welcome back to practical time series analysis, and welcome to week 3.
At this point in the course, we can do an awful lot,
and we're going to try to extend our skill set.
We deal first with the concept of stationarity.
Now, if you think about it, if you were to, this is a maybe silly example, but
if you had a bag of popcorn, and I'm thinking now of microwave popcorn,
but I think the same thing would work on the stove top as well.
If you start popping your popcorn, in the beginning,
you're not going to get a lot of action.
And then you're going to have a really busy time where there's a lot of action.
And then again, it'll trail off and you won't get very much action any more.
If you were to think about a sort of intensity function as you moved along,
then the intensity function would be pretty low in the beginning, and
then it would be pretty big in the middle and then get low again.
We would not think about that as a stationary process.
For a stationary process, we think of the time series or the stochastic process
as essentially being qualitatively similar as you look along the time series.
We'll discuss this in detail in the lectures coming up this week.
We'll also look at back shift operators, which is a mathematical notational
convenience, but like good notation, it will get some work done for us.
We'll use it when we discuss invertibility and duality.
We'd like to relate moving average and autoregressive processes.
So this week we study the autoregressive process in some detail,
and we take some times to look at the famous Yule-Walker equations.
These help us to relate the autocovariance structure of a time series or
stochastic process with the coefficients in that process.
Again, this will make more sense as we go through the lessons this week.
So, enjoy your week.