**Subject Code/Name:** MATH5845 - Time Series**Contact Hours:** 2 x 2hr lecture (no tutorials; some 'tute' questions covered in the lecture)

**Assumed Knowledge:** None explicitly stated, but just as with all level 3/5 statistics courses you should have foundation up to second year statistics (MATH2801/2901 level). Knowledge of linear models (MATH2831/2931) is highly recommended for one topic, but it only matters for that topic, and you only need to understand the linear model itself (don't worry about F-tests etc). MATH3801/3901/5901 not required,

**Assessment:** - 1 x 15% Assignment

- 1 x 20% Assignment

- 5% Class participation

- 60% Final exam

**Lecture Recordings?** Yes

**Notes/Materials Available**: Detailed lecture notes and lecture scribbles are given. Excerpts from textbooks given.

**Textbook:**- Shumway, R.H. and Stoffer, D.S. (2016) Time Series Analysis and Its Applications with R Examples, 4th edition, Springer-Verlag, New

York

- P. J. Brockwell & R. A. Davis (2002), Introduction to Time Series and Forecasting, Second Edition, Springer-Verlag, New York.

They're both good reads, but not needed.

**Lecturer(s):** Dr. Zdravko Botev

**Year & Trimester of completion:** 21 T2

**Difficulty:** 4.5/5

**Overall Rating:** 4.5/5

**Your Mark/Grade:** ~~93~~ 96 HD

**Comments: **This is one of many postgraduate statistics courses. Recently, it has remained on a yearly offering.

Time series branches off from stochastic process. It is the analysis of data that is indexed by a time variable. Time is assumed discrete in time series, because in practice although the phenomena may be continuous, you only collect it at discrete time intervals. In practice your time series data can be quite long (collect data over lots of timestamps), but you only study the data set itself. There is no comparison between two time series in this course.

The first thing to mention is that this is a Zdravko course. He teaches you the theory. It's more appropriate to think of this course (at least presently) as

*Theory of Time Series*. You'll be introduced autocovariance/autocorrelation, ARMA, spectral densities, etc. all from a mathematical standpoint. Of course, there are a couple questions that make you apply the theory to solving real problems/on real data sets, e.g. maximum likelihood of the ARMA parameters. For someone like me, this is exactly what I want. Yet somebody who only cares about applications may not be so interested.

The first half of the course introduces the mathematical background (including autocorrelation; quite surprisingly huge) needed for time series algorithm. The second half focuses on time series concepts, and develops the algorithms that typically get implemented for time series analysis.

Class participation is free marks - just contribute once (question OR answer) and you walk away with 5%. Quizzes are mostly free marks as well. Basically, the question bank gets released, and one question gets randomly selected for which you have to submit a response for. We had at least 1 week to prepare our answer for both the quizzes. The difficulty really comes from the final exam in my opinion (up till then, difficulty is something like 2.5/5).

In short, I just felt there was no time to answer everything. It was nice to know that out of the 4 questions given, we only needed to answer 3 such questions. Somehow, one of the three I picked was way too long. I remember submitting the exam with 26 or so seconds to spare; zero time to actually check my answers.

In terms of the coding, Zdravko supports at least Matlab, R, and Python. Choose any one of the three, and roll with it. (However, his live coding is in Matlab, because that's what he's more comfortable with.)

Despite being a theoretical course though, I would at least ask many postgrad students "why would you skip time series"? It's still pretty fundamental to know, in my opinion, as a working statistician. (Time series is also used in ML apparently, but I haven't investigated how.)