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Times Series Analysis

David Pupovac

Lazarski University

David Pupovac obtained his PhD in Political Science from Central European University in Budapest.

His main research interests are in applied statistics with an emphasis on electoral politics, voting behaviour and the radical right.

David teaches courses in quantitative methods and applied statistics at Lazarski University in Poland.

Course Dates and Times

Monday 25 February – Friday 1 March, 14:00 – 17:30 (finishing slightly earlier on Friday)
15 hours over five days

Prerequisite Knowledge

  • Basic statistical concepts
  • Linear regression models
  • The basics of inferential statistics
  • Basic R

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, contact the instructor before registering.

Short Outline

This course is a comprehensive introduction to time series analysis with R. You will gain an understanding of time series and learn how to meaningful inferences and forecasts from data collected over time.

I will successively introduce more complex aspects of statistical analysis, so the course is suitable for students who have a basic training in statistical analysis and for those who have a more advanced statistical background.

The course takes a hands-on approach to teaching the logic of analysis and estimation. I will present examples of application of techniques to the actual data, and you will perform a variety of data analyses.

By the end of the course, you will be able to select an appropriate method given a research question and time series data, and to interpret the results of the statistical analysis.

Tasks for ECTS Credits

2 credits (pass/fail grade) Attend at least 90% of course hours, participate fully in in-class activities, and carry out the necessary reading and/or other work prior to, and after, class.

3 credits (to be graded) As above, plus complete one task (tbc).

4 credits (to be graded) As above, plus complete two tasks (tbc).

Long Course Outline

Contemporary forms of data collection enable unprecedented access to data gathered over time. This type of data may encompass fast-changing series collected over short spans of time (such as stock prices) and slow-changing series collected across extended periods (such as the variation in quality of government over time). Consequently, the methods of analysing time series are applicable to a wide range of research questions and travel across disciplinary boundaries.

Time series models have specific assumptions and their application is driven by theoretical justification and the properties of data. This course will address these topics by gradually introducing more demanding concepts and techniques.

You will learn to select the statistical method best suited for addressing the particular research question given a specific data set, to employ and interpret statistical techniques, and to assess the empirical support for the argument.

Day 1

My first lecture introduces the concept of time series. It addresses the structure of this data type vis-à-vis other data types, and approaches the problem of time series data from the linear regression perspective. We discuss regression assumptions in detail, with the accent on the assumption violations with respect to autocorrelation. We cover the theoretical background of three statistical methods applicable to minor violations of classical regression models:

  • standard error correction – Newey-West estimator
  • OLS transformations
  • generalised least squares (GLS)

Day 2

We address the problem of time series from a univariate perspective. First, we discuss components of signal and variance decomposition, then I introduce a set of basic smoothers, with the emphasis on exponentially weighted moving average and forecasting. The crux of this session is the theory and application of one of the most influential time series models: ARMA. We will discuss autoregressive (AR) and moving average (MA) components in detail.

Day 3

We continue discussing ARMA, focusing on the concept of stationarity (ARIMA). This session addresses trend stationary and unit roots processes, and introduces methods such as the Dickey-Fuller test, and the autocorrelation and partial autocorrelation functions, among others.

Day 4

First, we go back over the material already covered. The remainder of the session broadens the discussion of the classical ARIMA model with respect to the introduction of independent variables (ARIMAX) and the introduction of seasonal component (SARIMA). If time allows, we will address the problem of heteroskedasticity in residuals via elaborating the autoregressive conditional heteroskedasticity model (ARCH).

Day 5

I introduce advanced time series models, in particular vector autoregressive (VAR) models. In contrast to previously discussed univariate and multivariate models, these models take a multi-equation approach to time series data sets. The lecture introduces three VAR models: simple VAR, recursive VAR and the vector error-correction model. You will learn how to establish the succession between events and verify causal relation in a statistical manner (Granger causality), and to understand and tackle the problem of cointegration.

Day Topic Details
Day 1 Introduction to time series analysis: Newey-West estimator, transformation, GLS

90min lecture, 90min lab

Day 2 Univariate time series: smoothers and ARMA

90min lecture, 90min lab

Day 3 Univariate time series: ARIMA

90min lecture, 90min lab

Day 4 Independent variables and the seasonal components in ARIMA context (ARIMAX and SARIMA)

90min lecture, 90min lab

Day 5 Vector autoregression: simple and recursive vector autoregression , and vector error correction model

90min lecture, 90min lab

Day Readings

Becketti, Sean (2013), Chapter 5


Cowpertwait, Metcalfe (2009), Chapter 1, 2, 3, 4;  Pfaff (2008), Chapter 1


Cowpertwait, Metcalfe (2009), Chapter 6 and 7


Cowpertwait, Metcalfe (2009), Chapter 7; Becketti, Sean (2013), Chapter 8


Cowpertwait, Metcalfe (2009), Chapter 11; Pfaff (2008) , Chapter 2, 3, 4, 7, 8; Becketti, Sean (2013), Chapter 9 and Chapter 11, Brandt, Williams (2007)

Software Requirements

Download the latest version of R (R 3.3) and RStudio 

Hardware Requirements

Bring your own laptop with R installed.

Any contemporary notebook computer that can run R is adequate.


Cowpertwait, Paul S.P. Metcalfe, Andrew (2009) Introductory Time Series with R, Springer

Pfaff, Bernhard (2008) Analysis of Integrated and Cointegrated Time Series with R, Springer

Becketti, Sean (2013) Introduction to Time Series Using Stata, StataCorp

Additional literature

Greene, William H. (2001) Econometric Analysis, Pearson Global Edition.

Wei, William W.S.  (2005), Time Series Analysis : Univariate and Multivariate Methods, Pearson Addison Wesley.

Shumway and Stoffer (2006) Time Series Analysis and Its Applications: With R Examples, Springer.

Baltagi, Badi H. (2011) Econometrics, Springer

Baltagi, Badi H. (2005) Econometric Analysis of Panel Data, John Willey and sons

Recommended Courses to Cover Before this One

<p><strong>Summer School</strong></p> <p>Introduction to R</p> <p>Introduction to Regression Analysis</p> <p>Advanced Topics in Applied Regression</p>

Recommended Courses to Cover After this One

<p><strong>Winter School</strong></p> <p>Multilevel Regression Modelling</p> <p>Panel Data Analysis: Hierarchical Structures, Heterogeneity and Serial Dependence</p>

Additional Information


This course description may be subject to subsequent adaptations (e.g. taking into account new developments in the field, participant demands, group size, etc). Registered participants will be informed in due time.

Note from the Academic Conveners

By registering for this course, you confirm that you possess the knowledge required to follow it. The instructor will not teach these prerequisite items. If in doubt, contact the instructor before registering.