Time Series Modelling
Coordinator AY 2026-2027
Prof. dr. Alain Hecq
a.hecq@maastrichtuniversity.nl
Module description
This course is intended for people in the field of economics/business who want a relatively non-technical (although correct) introduction to applied econometrics with a focus on modelling time series features and forecasting. By features I mean that time series have several characteristics such as a trend component, some dynamics, seasonality, volatility, breaks, etc. We need to discover those components (using econometric techniques, graphs, and tests statistics); we have to estimate them to be able to understand the mechanisms that have generated the data that we want to investigate and to forecast. Also, contrarily to cross section data you are familiar with, regressions with macroeconomic time series will probably lead to what is called spurious regressions. This means that everything you know about the interpretation of the results (t-tests, R-squared) might be misleading. So doing, blindly fitting the ”best” model using some automatic type of machine learning algorithms may give you the feeling that to have a very good model that however might dramatically fail when applied to a different period (e.g. future).
By relatively non-technical (i.e., applied econometrics focus) I mean that I do not do asymptotic theory, I do not derive the properties of estimators for instance but we use the appropriate tools. We do empirical analyses (using EViews) on real data (mine first and quickly yours next). The reason to start with some data that I provide is, that although you can easily download time series of your choice for inflation, GDP, etc., I would like first that we work on the same series to be sure that you have implemented tools correctly. This also allows you to get trained with EViews.
Remember that econometrics is useful
· (i) To test for economic theory (Does the Keynesian theoretical consumption function match with the observations collected in the Netherlands?),
· (ii) To quantifying economic relationships and co-movements (Do cuts in unemployment benefits decrease the unemployment rate?),
· (iii) to forecast economic indicators (What is next year inflation rate in Germany?) and
· (iv) To do economic policy simulations and stress tests (Will banks survive to a new financial crisis?)
We will focus more on (ii) and (iii) but have in mind that garbage in, garbage out. Indeed some data are "wrong" or non-accurate, e.g. typos, measurement errors. Models are misspecified, e.g. omitted variables in studying a relationship or spurious regressions. All models are wrong. Estimators (the way to get a quantity of interest) are not appropriate due to breaks, autocorrelation, endogeneity bias, heteroskedasticity, small sample issues,...
Economic theory helps to have an idea of the variables to include in a model; stat/econometrics is useful to try to get a model that meets some assumptions and to include statistically relevant variables. Our goal will be to get closer to the (unknown) way the data have been generated, namely the data generating process.
This course is mainly around the linear regression model and the ordinary least squares estimator (OLS). Hence, this is basically the prerequisite that you have to have to start this course. We introduce misspecification tests and evaluate the performances of our best models for expost and exante forecasts.
Material
I do not really have a book that I follow; I mainly use my slides (and my oral non-recorded lectures). I use some chapters in Diebold (2018), Forecasting. The book is available online (free download) at Diebold’s webpage at http://www.ssc.upenn.edu/~fdiebold/Textbooks.html. The book is quite easy and provides different examples than mines. You can catch up with econometrics for instance with Stock and Watson (2020), Introduction to Econometrics. We will also cover their Chapters 15, 16, 17.
Meetings
There are meetings on Wednesdays afternoon with both lectures and practical/empirical sessions. Each week you will have empirical investigations to prepare (team homework) and to present at the beginning of the meeting the week after. You will come to the board and show your main results (informal presentations, slides are not required).
Lecture slides of the corresponding week will be uploaded before the meetings (I hope the week before). In each week, we focus on topics according to the following draft schedule. The days are fixed but the content might change.
Week 1 (23/09): Introduction to time series features, importance of non stationarity, brush up econometrics, intro to EViews.
Week 2 (30/09): Mispecification tests: autocorrelation, heteroskedasticity, non normality, non linearity. Discussion of the case from Week 1.
Week 3 (7/10): Unit root tests (deterministic versus stochastic trends). Discussion of the case from Week 2.
Week 4 (21/10): Deterministic components: seasonality, outliers, breaks. Discussion of the case from Week 3.
Week 5 (4/11): Forecast comparison and combination. Discussion of the case from Week 4 material.
Week 6 (18/11): ARIMA modelling. Discussion of the case from Week 5 material.
Week 7 (25/11): Presentation of best univariate ARIMA models (20%).
Week 8 (02/12): Spurious regression and cointegration.
Week 9: (09/12) VARs and impulse responses. Discussion of the case from Week 8.
Week 10: (16/12): Final presentation and exam (50%).
Meetings/presentation
There will be at the beginning of each meeting (starting on week 2) a discussion of your results. They will be related to the material of the week before. Investigations will be carried out using EViews package. You will work with a teammate (2 people), and come to the board to show your results obtained on your own data.
Note that there exists a free lite student version at EViews website. That version is quite good but you cannot save your results if you modify your data for instance, namely you have to copy and paste outputs e.g. in Word. In addition, the size of the dataset is limited but that will be OK for us. Do not buy the student version, download the free lite version.
About EViews: my point of view. EViews is a very powerful dropdown menu econometric package (but not limited to the hundreds of estimators EViews proposes: there are add ins, programing tools). It is easy to use and very convenient to start with directly. It allows us to have the same output in class. You should know that many institutions do not authorize open sources packages (e.g. R depends on who did packages, there are mistakes, different layouts) and hence packages like STATA, MATLAB, SPSS, EViews, SAS are easier to trust by many companies. My advice for your real life activities would be to work with at least one of those econometric packages (again, we will use EViews) and one programing language (I use GAUSS and Julia myself but R, Python are OK). When you develop your own routine, check intermediary steps with a confirmed package. I finally think that it is better to learn several packages, not everyone will end in academia or in start up companies.
Examination
The final mark will be the sum of your participation during the block (30%). This includes your physical presence at discussion and the presentation of your weekly empirical output with your teammate. There will be an intermediate more serious presentation on the univariate model (20%) and the final empirical paper on which we will have an oral team discussion at the end (50%). No written exam.
Participation 30%: Active participation includes the study of the material, namely the preparation of the chapters, i.e. read assigned material (book chapters, slides) before/after (it depends on you actually) sessions start. Each week you will have an empirical investigation to prepare. Those assignments must be done in teams of two students. Starting week 2 to week 9, each team should upload the outcome of its investigations. You get 1 point if you upload your document with the outcomes of your team investigations (pdf, doc). I take into account whether you did it seriously, not that it is correct because this is what we check during our meetings. It’s important that your participate at discussion in person, not only that you did the case.
Intermediary presentation on ARMA (20%): On 25/11 You will have a more formal presentation on the material covered so far. Compared to the less formal weekly presentation, you should prepare slides with your main results, motivate your investigations, etc.
Paper 50%: There will be a final research paper (remaining 50%), to some extend the collection of your weekly investigations on the data of your choice (that will be explained in due course). This is to be done in groups of 2 students (same teammate or choose a different one in case of free riding) as well. The paper will be about: comparison of models, on data you chose, show that you picked up good models (no misspecifications), forecast comparisons and combinations,...There are no fixed bounds for the number of pages. Can be 20 pages, can be more with the appendix. You are free, you should convince me about the outcomes of your investigation.