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.