Welcome to practical time series analysis. Time series and their mathematical models, so called stochastic processes, form a really vibrant rich areas of study and research as well as being an area of real practical significance. So if you're a mathematician and you want to study elegance, then this is a nice course for you. You can get a good introduction into stochastic processes. But I suspect what's more likely true for many of the people in this course, if you're on the job and all of a sudden you have to look at time series data, and your mathematical background didn't include a study of time series or stochastic processes, this course will help give you a nice overview, a very practical approach to where time series come from and how people manage them. Let's take a look at what we're going to study in the course. We have a few categories here, but really the list goes on, it's almost endless. Many people, you can imagine, if you're looking at temperature data in Melbourne, Australia or if you'd like to know about earthquakes, many people need to deal with time series data. Perhaps you have sales figures, you're looking at stock prices. It's a very basic object, measuring a quantity in time and so it's very natural that many of us have to deal with time series. So that was the good news. This may be the bad news for some people, but maybe not. What do you need to be successful in this course? We're trying to do a course which is kind of honest and looking at the real complexities involved in time series, but keeping the mathematical preliminaries as modest as possible. So if you have calculus, let's say calculus two, not so much because we'll be integrating very much, but we'll be dealing with sequences and series. This is very natural, these are time series, then calculus would be a real plus. We're assuming that you've done at least a little bit of inferential statistics. You've done a hypothesis test, you've done some descriptive statistics, so you can do a box plot, these sorts of things. We spent time during the first week looking at these basics in some depth, so if it's been a long time since you've done any statistics, don't let that be too off putting, come on in and see if you can be productive. But we do assume that you have some background. Also if you're dealing with time series, you could be doing this with Excel or in our course we assume that you have access to R, which is free, you download it off the Internet. We assume that you're and comfortable in computers, and that if we ask you to go get a data set from a website, that that'll be within your wheel house, so to speak. So we're going to be doing a little bit of programming, but ours is more a scripting environment. We're not going to be writing elaborate codes, but we will be calling functions in order to analyze our data. In the first week then, we get started in R, we'll figure out how to download the program, how to install it on your computer, whether you're on Windows or Mac, and how to start working with packages. We'll go back and review some of the basic stats you might have to taken in a stats 100 course at some point. And in particular we'll look at regression and correlation. In the second week we start visualizing our time series and also doing modelling. So we like to think about mathematical models for time series because we can study the properties of mathematical models in a very nice and general way, and then take our insight and bring them to bear on the actual time series that we have in front of us. We'll deal with autocorrelation and autocovariance. This is one of the truly fundamental ideas in stochastic processes and time series. And we'll look at some famous examples, random walks, moving averages. In the third week, we start dealing with the concept called Stationarity, which essentially if we can assume it, it'll help us to do our modelling much more efficiently, much more obviously. We'll continue to look at examples. We'll get into a little bit of the Mathematics with our Backshift Operator, we'll look at series, duality, invertibility. So don't let that be too off putting. In Week 4, we continue the modeling process, and try to think about mathematical objects that will give rise to time series data. Much like you can think of a random variable as modelling the toss of a coin. So we'll deal with moving average processes, autoregressive processes, Yule Walker, we'll study the partial autocorrelation coefficient, to try to figure out from a given time series what the model might have been that produced it. Since we are trying to model, we're trying to write the story that gives rise to our time series. We'll deal with model quality. And there are a number of ways to measure this. The Akaike information criterion being one of them. We'll look at autoregressive, moving average, autoregressive moving average, integrated autoregressive moving average models. We'll start thinking about how to put in trends and seasonality sort of data. And so in Week 6 you can see Seasonality takes center stage. There is a set of ideas that were developed in the 1950s, but people still find really, really useful. Holt and Winters are two names of famous mathematicians that you'll see associated with this, where we can start doing forecasting. Based upon past data, can we start making some good guesses about what we're going to see next week, next month or next year? And so we get into the single, double and triple exponential smoothing. We hope you enjoy the course, and welcome.
