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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 5 to Friday 9 March 2018
15 hours over 5 days

Prerequisite Knowledge

The participants need to be familiar with basic statistical concepts, have knowledge of linear regression model and have understanding of the basics of inferential statistics.

The students need to have the basic knowledge of  R.

Short Outline

The course provides a comprehensive introduction to time series analysis with R. The goal of the course is to provide participants with understanding of time series and train them in extracting meaningful inferences and forecasts from data collected over time. As it will successively introduce more complex concepts and aspects of statistical analysis, the course is suitable for both students who have a basic training in statistical analysis and students who have a more advanced statistical background. The course will cover the logic of analysis and estimation; however the emphasis is on hands on approach. The examples of application of techniques to the actual data will be presented in class, and students will perform a variety of data analyses. By the end of the course, participants are expected to be able to select appropriate method given a research question and a time series data, and interpret the  results of the statistical analysis.

Tasks for ECTS Credits

  • Participants attending the course: 2 credits (pass/fail grade) The workload for the calculation of ECTS credits is based on the assumption that students attend classes and carry out the necessary reading and/or other work prior to, and after, classes.
  • Participants attending the course and completing one task (see below): 3 credits (to be graded)
  • Participants attending the course, and completing two tasks (see below): 4 credits (to be graded)

Long Course Outline

The contemporary forms of data collection enable unprecedented access to data gathered over time. This type of data may encompass both 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 both theoretical justification and the properties of data. The course will address these topics by gradually introducing more demanding concepts and techniques. The participants will be trained to select the statistical method best suited for addressing the particular research question given a specific data set, employ and interpret statistical techniques, and assess the empirical support for the argument.

Day 1

The first lecture introduces students to the concept of time series and addresses the structure of this data type vis-à-vis other data types. It approaches the problem of time series data from the linear regression perspective. In this regard, regression assumptions are discussed in detail while the accent is on the assumption violations with respect to autocorrelation. The course further proceeds to teach participants the theoretical background of three statistical methods (standard error correction – Newey-West estimator, OLS transformations, and generalized least squares - GLS) which are applicable to minor violations of classical regression model.

Day 2

The second lecture addresses the problem of time series from univariate perspective. The session is initiated by discussing components of the signal and variance decomposition. Subsequently, participants are introduced to a set of basic smoothers, where the emphasis is placed on exponentially weighted moving average and forecasting. However, the crux of the session is on the theory and the application of one of the historically most influential time series models: ARMA/ARIMA. In particular, the emphasis of the class will be on discussing autoregressive (AR) and moving average (MA) components in detail.

Day 3

The third lecture continues the discussion of ARMA by focusing on concept of the stationarity and ARIMA. Consequently, this session addresses concepts such as trend stationary and unit roots processes, and introduces techniques and methods such as Dickey-Fuller test, autocorrelation function, partial autocorrelation function and others. In addition, a major portion of the class is dedicated to identification of time series processes.

Day 4

The fourth lecture broadens discussion of ARIMA. Firstly, we introduce the seasonal component in time series modelling and the respective modification of ARIMA (SARIMA). Secondly, extensions of the classical ARIMA model are discussed with respect to the introduction of independent variables (ARIMAX). The session is finalized with the discussion of the problem of endogeneity and the introduction to the simultaneous equations models and the issues related to their estimation.

Day 5

The goal of the last session is to introduce the participants to advanced time series models and, in particular vector autoregressive (VAR) models. In contrast to previously discussed univariate and multivariate models, these models introduce multi-equation approach to time series data sets. The lecture introduces three VAR models: simple VAR, recursive VAR and vector error-correction model. Furthermore, the module teaches participants how to establish the succession between the events and verify causal relation in statistical manner (Granger causality). In addition, it enables them to understand and tackle problem of cointegration.

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

90min lecture, 90min lab

2 Univariate time series: smoothers and ARMA

90min lecture, 90min lab

3 Univariate time series: ARIMA

90min lecture, 90min lab

4 Extensions of ARIMA: ARIMAX, SARIMA, simultaneous equations models

90min lecture, 90min lab

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

Latest version of R (R 3.3) and RStudio. R is freely available at

Hardware Requirements

Participants need to bring their own laptop with R installed. Any contemporary notebook computer that can run R will be adequate.


Brandt, Williams (2007) Multiple Time Series Models, SAGE Publications Inc

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

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 the Use of 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 at the time of change.

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, please contact us before registering.