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570 Chapter 14 Introduction to Time Series Regression and Forecasting

coefficients has a causal interpretation. From the perspective of forecasting, what
is important is that the model provides as accurate a forecast as possible. Although
there is no such thing as a perfect forecast, regression models can nevertheless
provide forecasts that are accurate and reliable.

The applications in this chapter differ from the test score/class size prediction
problem because this chapter focuses on using time series data to forecast future
events. For example, the parent actually would be interested in test scores next
year, after his or her child had enrolled in a school. Of course, those tests have not
yet been given, so the parent must forecast the scores using currently available
information. If test scores are available for past years, then a good starting point
is to use data on current and past test scores to forecast future test scores. This
reasoning leads directly to the autoregressive models presented in Section 14.3, in
which past values of a variable are used in a linear regression to forecast future
values of the series. The next step, which is taken in Section 14.4, is to extend
these models to include additional predictor variables such as data on class size.
Like Equation (14.1), such a regression model can produce accurate and reliable
forecasts even if its coefficients have no causal interpretation. In Chapter 15, we
return to problems like that faced by the school superintendent and discuss the
estimation of causal effects using time series variables.

14.2 Introduction to Time Series Data
and Serial Correlation

This section introduces some basic concepts and terminology that arise in time
series econometrics. A good place to start any analysis of time series data is by
plotting the data, so that is where we begin.

Real GDP in the United States

Gross Domestic Product (GDP) measures the value of goods and services pro-
duced in an economy over a given time period. Figure 14.1 a plots values of “real”
GDP per year in the United States from 1960 through 2012, where “real” indicates
that the values have been adjusted for inflation. The values of GDP are expressed
in $1996, which means that the price level is held fixed at its 1996 value. Because
U.S. GDP grows at approximately an exponential rate, Figure 14.1 a plots GDP
on a logarithmic scale. GDP increased dramatically over a recent 52-year period,
from approximately $3 trillion in 1960 to over $15 trillion in 2012. Measured on a
logarithmic scale, this five-fold increase corresponds to an increase of 1.6 log points.