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C h a p t e r Introduction to Time Series

14 Regression and Forecasting

T ime series data—data collected for a single entity at multiple points in time—
can be used to answer quantitative questions for which cross-sectional data are
inadequate. One such question is, what is the causal effect on a variable of interest,
Y, of a change in another variable, X, over time? In other words, what is the dynamic
causal effect on Y of a change in X ? For example, what is the effect on traffic fatalities
of a law requiring passengers to wear seatbelts, both initially and subsequently, as
drivers adjust to the law? Another such question is, what is your best forecast of the
value of some variable at a future date? For example, what is your best forecast of
next month’s unemployment rate, interest rates, or stock prices? Both of these
questions—one about dynamic causal effects, the other about economic forecasting—
can be answered using time series data. But time series data pose special challenges,
and overcoming those challenges requires some new techniques.

This chapter and Chapters 15 and 16 introduce techniques for econometric
analysis of time series data and apply these techniques to the problems of forecast-
ing and estimating dynamic causal effects. This chapter introduces the basic con-
cepts and tools of regression with time series data and applies them to economic
forecasting. Chapter 15 applies the concepts and tools developed in this chapter to
the problem of estimating dynamic causal effects using time series data. Chapter 16
takes up some more advanced topics in time series analysis, including forecasting
multiple time series and modeling changes in volatility over time.

The empirical problem studied in this chapter is forecasting the growth rate of
U.S. Gross Domestic Product (GDP)—that is, the percentage increase in the value of
goods and services produced in the U.S. economy. While in a sense forecasting is
just an application of regression analysis, forecasting is quite different from the esti-
mation of causal effects, the focus of this book until now. As discussed in Section
14.1, models that are useful for forecasting need not have a causal interpretation: If
you see pedestrians carrying umbrellas, you might forecast rain, even though carry-
ing an umbrella does not cause rain. Section 14.2 introduces some basic concepts of
time series analysis and presents some examples of economic time series data.
Section 14.3 presents time series regression models in which the regressors are past
values of the dependent variable; these “autoregressive” models use the history of
GDP to forecast its future. Often, forecasts based on autoregressions can be

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