So in this lecture, we are going to start with answering a very basic question What is a Time series?
Now you may have some intuition about what a Time series is.
For example, the price of a stock or readings from an EKG.
The weather is at other simple, everyday example of a time series that everyone can recognize.
So it's clear that time series data is all around us.
You don't need to be a data scientist to understand intuitively what a Time series is.
But for the purpose of this class, we're going to get a bit more specific.
Let's talk about some things we will not discuss in this class.
One thing we won't discuss is sequence data.
In general, time series data is one kind of sequence data, but sequence data encompasses more than
just time series.
For example, the sentences I'm speaking right now are sequences of words.
We have techniques for dealing with sequences of words from the field of NLP.
Another similar example is genomics data.
You and I are made up of sequences the letters C and G, which represent special molecules or sequences
which are kind of like computer programs for living things.
So the difference between this class and these examples is that these examples are categorical words,
and molecules are not numerical objects, although they form sequences just like a time series.
In this class, A Time series consists of real valued observations.
Now, one side note to keep in mind, though, is that many of the techniques in this course can be
applied to categorical sequences as well.
So here's another example of something we will not cover in this class.
So suppose you have an Apple Watch and every now and then you check your heart rate.
Now, let's say you keep these in some kind of Excel spreadsheet, but you're not very consistent.
So you might have three recordings this week, two recordings the previous week and so forth.
Furthermore, these readings are never taken at the same time.
In other words, these recordings take place at irregularly spaced intervals.
So there are a few techniques to handle irregularly spaced time series, but many more that do not.
Thus, in this class, we'll stick to models that handle discrete time time series sampled at regularly
spaced intervals.
Okay, so for the purpose of this class, a Time series is continuous, valued but discrete in time.
So before we end this lecture, there is one more kind of time series we should consider, which is
a vector time series.
In fact, vector time series are quite common.
We mentioned stock prices earlier, but as we all know, there are many stocks to choose from.
So the collection of stock prices of multiple stocks at each point in time would be a vector time series.
Or you can just have one stock with multiple indicators for each point in time.
And that's another example of a vector time series.
So another one of my favorite examples is brain signals.
Brain machine interfaces might sound futuristic, but in fact some rudimentary examples already exist.
Neuralink is one company whose goal is to improve this technology far beyond what we currently have.
So far, they've built this kind of sewing machine that will implant electrodes in your brain while
being minimally invasive.
So the main idea behind this technology is that your brain works by sending electrical signals between
neurons.
In fact, we'll explore this idea further when we study deep neural networks.
Now, these electrodes can read voltages from different parts of your brain which signal what kind of
activity is going on.
Theoretically, these signals can be decoded in order to read your thoughts.
So, for example, using this technology, we're able to train monkeys to control a computer mouse using
only their minds.
It's also possible not just to read from the brain, but to write to the brain.
Once this technology is perfected, we'll be able to send information to the mind.
So you might, for example, read a book or learn guitar without actually having to pick up that book
or guitar.
And of course, this is an example of a vector time series since there are multiple electrodes, all
reading voltages periodically.