# Time Series Analysis - Introduction

Course description

Many of the data sets that social scientists analyze are organized over time including leader approval, GDP per capita, homicide rates, and political violence. While many of the tools that students learn in regression courses are useful for analyzing time series data, there are several unique properties of time series data that must be understood before working with such data. This course provides an introduction to methods of time series analysis, building upon students’ background knowledge in statistical inference and regression analysis. We will begin with basic descriptive methods for viewing time series data and then talk about stationarity assumptions and how violations of these assumptions threaten inferences in regression analyses of time series data. Students will also learn about autoregressive integrated moving average (ARIMA) models, including autocorrelation (ACF) and partial autocorrelation (PACF) functions. We will review several statistical tests for unit roots, serial correlation, and normality. Students will be introduced to regression based time series models, such as the autoregressive distributed lag (ADL) model, as well as more advanced models such as the error correction and GARCH models. We will also learn about modeling interventions in time series data.

Prerequisites (knowledge of topic)

Students should be familiar with basic regression analysis (e.g. Regression I or similar course that covers bivariate and multivariate regression models, assumptions, and residual diagnostic tests) and the fundamentals of statistical inference (e.g. hypothesis testing with t/z scores, sampling distributions).

Hardware

The assignments can be completed on the computers in the computer lab rooms or on a student’s personal computer if they have the required software.

Software

The primary statistical program for the course is STATA. The instructor can also provide sample code for the assignments in R. The instructor will provide time series datasets that you can use for the assignments.

Structure

Day 1:  Introduction to Time Series Analysis & Univariate Time Series Tests

BFHP, Chapter 1 and Chapter 5

Topics: properties/types of time series data, graphical displays for time series (ts plot, histogram, Q-Q plot, etc), lag/differencing operators, approaches to time series analysis (LSE, Minnesota, etc), stationarity, unit root tests (DF, ADF, Phillips-Perron, etc.)

Day 2:  ARIMA Models

BFHP, Chapter 2, pp. 22-58 and Appendix, pp. 219-261

Topics: Trend stationarity vs. difference stationarity, Weak/strong stationarity, random walk, unit roots, detrending, normality, Autocorrelation function (ACF), Partial autocorrelation function (PACF), AR processes, MA processes, ARIMA models (theoretical, empirically estimated models), model fit statistics (e.g. AIC, SBC), forecasting

Day 3:  Regression/Intervention Analysis & Structural Breaks

BFHP, Chapter 2, pp. 58-67 and Chapter 3

Topics: panel unit root tests (e.g. LLC, IPS, fisher), intervention analysis (abrupt vs. gradual, temporary vs. permanent), short run/long run effects, impulse response function, impact assessment model, pre-whitening, transfer function models, cross-autocorrelation function (CACF), distributed lag models (Koyck, Almon, exponential, etc.), multipliers (e.g. impact, interim, total), OLS time series models (assumptions), serial correlation, GLS models

Day 4:  ARCH/GARCH Models and Granger Causality

BFHP, Chapter 4 and Chapter 7, pp. 181-187

Topics: Exogeneity (conditional & marginal models; weak vs. strong), Granger Causality (GC) tests & examples, panel GC tests, Autoregressive Conditional Heteroskedastic Models (ARCH/GARCH/TGARCH, IGARCH, etc), GARCH example in STATA

Day 5:  Error Correction Models and Vector Autoregression (VAR)

BFHP, Chapter 6

Topics: cointegration (tests-e.g. Johansen), Granger Representation Theorem, error correction model (ECM), ECM model of US presidential approval, VAR models (structural, recursive, Bayesian, etc), structural equation models, reduced form, steps for VAR analysis (unit root tests, lag length tests, estimation of VAR, GC tests, FEVD, Impulse response analysis, residual diagnostics), empirical examples for VAR

Literature

Mandatory

Box-Steffensmeier, Janet M., John R. Freeman, Matthew P. Hitt, and Jon C.W. Pevehouse. 2014. Time Series Analysis for the Social Sciences. Cambridge University Press.

Supplementary / voluntary

Enders, Walter. 2010. Applied Econometric Time Series, 4th Edition. New York: Wiley.