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Welcome back to practical time series
analysis, and welcome to week 3.

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At this point in the course,
we can do an awful lot,

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and we're going to try
to extend our skill set.

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We deal first with
the concept of stationarity.

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Now, if you think about it, if you were
to, this is a maybe silly example, but

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if you had a bag of popcorn, and
I'm thinking now of microwave popcorn,

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but I think the same thing would
work on the stove top as well.

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If you start popping your popcorn,
in the beginning,

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you're not going to get a lot of action.

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And then you're going to have a really
busy time where there's a lot of action.

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And then again, it'll trail off and
you won't get very much action any more.

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If you were to think about a sort of
intensity function as you moved along,

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then the intensity function would
be pretty low in the beginning, and

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then it would be pretty big in
the middle and then get low again.

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We would not think about that
as a stationary process.

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For a stationary process, we think of
the time series or the stochastic process

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as essentially being qualitatively similar
as you look along the time series.

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We'll discuss this in detail in
the lectures coming up this week.

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We'll also look at back shift operators,
which is a mathematical notational

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convenience, but like good notation,
it will get some work done for us.

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We'll use it when we discuss
invertibility and duality.

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We'd like to relate moving average and
autoregressive processes.

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So this week we study the autoregressive
process in some detail,

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and we take some times to look at
the famous Yule-Walker equations.

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These help us to relate the autocovariance
structure of a time series or

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stochastic process with
the coefficients in that process.

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Again, this will make more sense as
we go through the lessons this week.

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So, enjoy your week.