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.