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Welcome to our first week in
Practical Time Series Analysis.

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As we get started in our course,
we'll need a software environment.

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We've chosen to use R in this course
because it's free, it's very high quality,

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and many people are working around
the world to come up with good packages,

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ways that you can extend the base R
system and accomplish your goals.

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We find that R is especially
good in time series analysis.

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So as we get started,
we'll learn how to download and install R.

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Many of us will probably already
have it available on our systems.

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We'll get used to working with R by
doing some basic descriptive statistics.

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And we'll learn how to pull
down these packages in R so

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we can extend the power of our program.

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Once our software environment is up and
available to us,

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we'll get started by doing some
basic numerical descriptions.

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This is really just so

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that we're all on the same page
in how to use the environment.

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We assume you've already seen 5 number
summaries, standard deviations, etc.

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Now, a time series is really just
a collection of data points.

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And so we can aggregate them and
look at a histogram, or

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we can view them in time and
look at a time plot.

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It's really, really important to get into
the habit whenever you have a time series

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of getting a quick,
graphical look at your time series.

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Within the world of
inferential statistics,

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we'll review straight-line regression.

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We'll look at regression models and
diagnostics.

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And these are tools that will help us
as we're exploring time series later.

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T-tests are brought in, again, as a review
because we'd like to do some inference.

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And we'll begin working with correlation.

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We assume you've seen correlation
in a basic stats course, but

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correlation is really one of
the cornerstones of time series analysis.

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Now, one usually thinks of a time-series
as a realization, as a dataset let's say,

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derived from a mathematical object
called the stochastic process.

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When we describe this mathematical
objects, we bring in terms like, for

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instance, stationarity.

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We need to get some traction, we need some
mathematical structure if we're going to

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say anything interesting
about our time series.

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And so we look at strong stationarity,
which would

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certainly make our lives easy if it
were true in our particular situation.

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But we often find that the data sets
presents it in business, economics,

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nature, science,
don't exhibit strong stationarity.

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But they do exhibit weak stationarity,
or at least approximately so.

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So we'll see how we can relax
the requirements of strong stationarity

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to that of weak in order
to get some work done.

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We'll look at autocovariance and
autocorrelation.

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These are functions that allow us to get
good descriptions of our time series.

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We start looking at some individual
expressions of stochastic processes.

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For instance, we'll look at random walks,
we'll look at moving average processes,

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and we'll develop these
ideas as the course unfolds.

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In order to have a place to
essentially play, we'd like to,

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right from the first week,
get across the idea of simulation.

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Given a mathematical model, we'll try to
use software in order to create a data set

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that exhibits the properties
that we think are important.

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Again, welcome to Week one, and
we hope you enjoy the course.