Times Series Analysis

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.

• 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.