Times Series Analysis

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.

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.