Two common trend removal or de-trending procedures are first differencing
and time-trend regression. First differencing is appropriate for I(1)
time series and time-trend regression is appropriate for trend stationary
I(0) time series. Unit root tests can be used to determine if trending data
should be first differenced or regressed on deterministic functions of time
to render the data stationary. Moreover, economic and finance theory often
suggests the existence of long-run equilibrium relationships among nonstationary
time series variables. If these variables are I(1), then cointegration
techniques can be used to model these long-run relations. Hence, pre-testing
for unit roots is often a first step in the cointegration modeling discussed
in Chapter 12. Finally, a common trading strategy in finance involves exploiting
mean-reverting behavior among the prices of pairs of assets. Unit
root tests can be used to determine which pairs of assets appear to exhibit
mean-reverting behavior.