Welcome to our first week in
Practical Time Series Analysis. As we get started in our course,
we'll need a software environment. We've chosen to use R in this course
because it's free, it's very high quality, and many people are working around
the world to come up with good packages, ways that you can extend the base R
system and accomplish your goals. We find that R is especially
good in time series analysis. So as we get started,
we'll learn how to download and install R. Many of us will probably already
have it available on our systems. We'll get used to working with R by
doing some basic descriptive statistics. And we'll learn how to pull
down these packages in R so we can extend the power of our program. Once our software environment is up and
available to us, we'll get started by doing some
basic numerical descriptions. This is really just so that we're all on the same page
in how to use the environment. We assume you've already seen 5 number
summaries, standard deviations, etc. Now, a time series is really just
a collection of data points. And so we can aggregate them and
look at a histogram, or we can view them in time and
look at a time plot. It's really, really important to get into
the habit whenever you have a time series of getting a quick,
graphical look at your time series. Within the world of
inferential statistics, we'll review straight-line regression. We'll look at regression models and
diagnostics. And these are tools that will help us
as we're exploring time series later. T-tests are brought in, again, as a review
because we'd like to do some inference. And we'll begin working with correlation. We assume you've seen correlation
in a basic stats course, but correlation is really one of
the cornerstones of time series analysis. Now, one usually thinks of a time-series
as a realization, as a dataset let's say, derived from a mathematical object
called the stochastic process. When we describe this mathematical
objects, we bring in terms like, for instance, stationarity. We need to get some traction, we need some
mathematical structure if we're going to say anything interesting
about our time series. And so we look at strong stationarity,
which would certainly make our lives easy if it
were true in our particular situation. But we often find that the data sets
presents it in business, economics, nature, science,
don't exhibit strong stationarity. But they do exhibit weak stationarity,
or at least approximately so. So we'll see how we can relax
the requirements of strong stationarity to that of weak in order
to get some work done. We'll look at autocovariance and
autocorrelation. These are functions that allow us to get
good descriptions of our time series. We start looking at some individual
expressions of stochastic processes. For instance, we'll look at random walks,
we'll look at moving average processes, and we'll develop these
ideas as the course unfolds. In order to have a place to
essentially play, we'd like to, right from the first week,
get across the idea of simulation. Given a mathematical model, we'll try to
use software in order to create a data set that exhibits the properties
that we think are important. Again, welcome to Week one, and
we hope you enjoy the course.