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Welcome to practical time series analysis.

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Time series and their mathematical models,
so called stochastic processes,

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form a really vibrant
rich areas of study and

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research as well as being an area
of real practical significance.

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So if you're a mathematician and

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you want to study elegance,
then this is a nice course for you.

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You can get a good introduction
into stochastic processes.

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But I suspect what's more likely true for
many of the people in this course,

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if you're on the job and all of a sudden
you have to look at time series data, and

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your mathematical background didn't
include a study of time series or

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stochastic processes, this course will
help give you a nice overview, a very

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practical approach to where time series
come from and how people manage them.

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Let's take a look at what we're
going to study in the course.

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We have a few categories here, but really
the list goes on, it's almost endless.

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Many people, you can imagine, if you're
looking at temperature data in Melbourne,

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Australia or
if you'd like to know about earthquakes,

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many people need to deal
with time series data.

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Perhaps you have sales figures,
you're looking at stock prices.

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It's a very basic object,
measuring a quantity in time and so

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it's very natural that many of us
have to deal with time series.

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So that was the good news.

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This may be the bad news for
some people, but maybe not.

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What do you need to be
successful in this course?

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We're trying to do a course
which is kind of honest and

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looking at the real complexities
involved in time series, but

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keeping the mathematical
preliminaries as modest as possible.

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So if you have calculus, let's say
calculus two, not so much because

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we'll be integrating very much, but we'll
be dealing with sequences and series.

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This is very natural,

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these are time series,
then calculus would be a real plus.

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We're assuming that you've done at least
a little bit of inferential statistics.

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You've done a hypothesis test,
you've done some descriptive statistics,

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so you can do a box plot,
these sorts of things.

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We spent time during the first
week looking at these basics

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in some depth, so if it's been a long
time since you've done any statistics,

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don't let that be too off putting, come
on in and see if you can be productive.

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But we do assume that you
have some background.

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Also if you're dealing with time series,
you could be doing this with Excel or

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in our course we assume that you
have access to R, which is free,

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you download it off the Internet.

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We assume that you're and
comfortable in computers, and

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that if we ask you to go get
a data set from a website,

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that that'll be within your wheel house,
so to speak.

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So we're going to be doing
a little bit of programming,

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but ours is more a scripting environment.

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We're not going to be
writing elaborate codes,

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but we will be calling functions
in order to analyze our data.

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In the first week then, we get started
in R, we'll figure out how to download

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the program, how to install it on your
computer, whether you're on Windows or

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Mac, and
how to start working with packages.

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We'll go back and review some of the basic
stats you might have to taken in

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a stats 100 course at some point.

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And in particular we'll look
at regression and correlation.

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In the second week we start visualizing
our time series and also doing modelling.

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So we like to think about
mathematical models for

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time series because we can study
the properties of mathematical models

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in a very nice and general way,
and then take our insight and

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bring them to bear on the actual time
series that we have in front of us.

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We'll deal with autocorrelation and
autocovariance.

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This is one of the truly fundamental ideas
in stochastic processes and time series.

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And we'll look at some famous examples,
random walks, moving averages.

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In the third week, we start dealing
with the concept called Stationarity,

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which essentially if we can assume it,
it'll help us to do our modelling

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much more efficiently,
much more obviously.

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We'll continue to look at examples.

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We'll get into a little bit of the
Mathematics with our Backshift Operator,

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we'll look at series,
duality, invertibility.

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So don't let that be too off putting.

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In Week 4,
we continue the modeling process, and

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try to think about mathematical objects
that will give rise to time series data.

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Much like you can think of a random
variable as modelling the toss of a coin.

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So we'll deal with moving average
processes, autoregressive processes,

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Yule Walker, we'll study the partial
autocorrelation coefficient,

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to try to figure out from a given time
series what the model might have been that

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produced it.

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Since we are trying to model,

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we're trying to write the story
that gives rise to our time series.

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We'll deal with model quality.

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And there are a number
of ways to measure this.

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The Akaike information
criterion being one of them.

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We'll look at autoregressive, moving
average, autoregressive moving average,

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integrated autoregressive
moving average models.

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We'll start thinking about how to put
in trends and seasonality sort of data.

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And so in Week 6 you can see
Seasonality takes center stage.

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There is a set of ideas that
were developed in the 1950s,

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but people still find really,
really useful.

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Holt and Winters are two names
of famous mathematicians

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that you'll see associated with this,
where we can start doing forecasting.

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Based upon past data, can we start making
some good guesses about what we're

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going to see next week,
next month or next year?

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And so we get into the single,
double and triple exponential smoothing.

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We hope you enjoy the course, and welcome.