192 The Basics of financial economeTrics
regression equation. The issue becomes more complex when the trend is sto-
chastic. As defined in Chapter 5, a stochastic trend is a persistent but random
long-term movement. Thus a variable with a stochastic trend may exhibit
prolonged long-run increases followed by prolonged long-run declines and
perhaps another period of long-term increases.
Most financial theorists believe stochastic trends better describe the
behavior of financial variables than deterministic trends. For example, if
stock prices are rising, there is no reason to believe they will continue to
do so in the future. Or, even if they continue to increase in the future, that
they may not do so at the same growth rate as in the past. This is because
stock prices are driven by a variety of economic factors and the impact of
these factors may change over time. One way of capturing these common
stochastic trends is by using an econometric technique usually referred to as
cointegration.
In this chapter, we explain the concept of cointegration. There are two
major ways of testing for cointegration. We outline both econometric meth-
ods and the underlying theory for each method. We illustrate the first tech-
nique with an example of the first type of cointegration problem, testing
market price efficiency. Specifically, we examine the present value model of
stock prices. We illustrate the second technique with an example of the sec-
ond type of cointegration problem, examining market linkages. In particu-
lar, we test the linkage and the dynamic interactions among stock market
indices of three European countries.
Stationary and Nonstationary Variables and Cointegration
The presence of stochastic trends may lead a researcher to conclude
that two economic variables are related over time when in fact they are
not. This problem is referred to as spurious regression. For example,
during the 1980s the U.S. stock market and the Japanese stock market
were both rising. An ordinary least squares (OLS) regression of the U.S.
Morgan Stanley Stock Index on the Japanese Morgan Stanley Stock Index
( measured in U.S. dollars) for the time period 1980−1990 using monthly
data yields
Japanese Stock index= 76.74+19 U.S. Stock Index
t-statistic (−13.95) (26.51) R^2 = 0.86The t-statistic on the slope coefficient (26.51) is quite large, indicating a
strong positive relationship between the two stock markets. This strong