# 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

Required Reading

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

Required Reading

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

Reading

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

Required Reading

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)

Required Reading

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, 4*^{th}* Edition*. New York: Wiley.

**Mandatory readings before course start**

none

**Examination**

The course grade is based on two homework assignments (50% of total grade each); the first assignment will involve estimating unit root tests and ARIMA models, while the second assignment involves estimating autoregressive distributed lag (ADL) models. The assignments can be submitted anytime up to two weeks after the course ends.

**Work load**

At least 24 units 45 minutes each on 5 consecutive days.