194 The Basics of financial economeTrics
our focus, we note that cointegration analysis has been used for mainly two
types of problems in finance. First, it has been used to evaluate the price
efficiency of financial markets in a wide variety of contexts. For example,
Enders used cointegration to evaluate the validity of Purchasing Power Par-
ity Theory.^2 As another example, Campbell and Shiller used cointegration
to test both the rational expectations theory of the term structure of interest
rates and the present value model of stock prices.^3 The second type of coin-
tegration study investigates market linkages. For example, there have been
a good number of studies that have looked at the linkage between equity
markets of different countries and regions.^4
Before explaining cointegration it is first necessary to distinguish
between stationary and nonstationary variables. A variable X is said to be
stationary (more formally, weakly stationary) if its mean and variance are
constant and its autocorrelation depends on the lag length, that is,
Constant mean: E(Xt) = μ
Constant variance: var(Xt) = σ^2
Autocorrelation depends on the lag length: cov(Xt, Xt−l) = γ(l)Stationary means that the variable X fluctuates about its mean with con-
stant variation. Another way to put this is that the variable exhibits mean
reversion and so displays no stochastic trend. In contrast, nonstationary
variables may wander arbitrarily far from the mean. Thus, only nonstation-
ary variables exhibit a stochastic trend.
(^2) Walter Enders, “ARIMA and Cointegration Tests of Purchasing Power Parity,”
Review of Economics and Statistics 70 (1988): 504−508.
(^3) John Campbell and Robert Shiller, “Stock Prices, Earnings and Expected Divi-
dends,” Journal of Finance 43 (1988): 661−676.
(^4) See, for example, Theodore Syriopoulos, “International Portfolio Diversification
to Central European Stock Markets,” Applied Financial Economics 14 (2004):
1253 −1268; Paresh K. Narayan and Russell Smyth, “Modeling the Linkages
between the Australian and G7 Stock Markets: Common Stochastic Trends and
Regime Shifts,” Applied Financial Economics 14 (2004): 991−1004; Eduardo D.
Roca, “Short-Term and Long-Term Price Linkages between the Equity Markets of
Australia and Its Major Trading Partners,” Applied Financial Economics 9 (1999):
501 −511; Angelos Kanas, “Linkages between the US and European Equity Mar-
kets: Further Evidence From Cointegration Tests,” Applied Financial Economics 8
(1999): 607−614; Kenneth Kasa, “Common Stochastic Trends in International Stock
Markets,” Journal of Monetary Economics 29 (1992): 95−124; and, Mark P. Taylor
and Ian Tonks, “The Internationalization of Stock Markets and Abolition of UK
Exchange Control,” Review of Economics and Statistics 71 (1989): 332−336.