Cointegration - evidence of long-run or equilibrium relationships: yt = a + b*xt + u
With cointegration the residuals (i.e., u) from a regression are stationary.
Provided two time series are cointegrated, the short-term disequilibrium
relationship between them can always be expressed in the error correction form.
Engle-Granger Two-Step approach
(1) Estimate long run relationship between yt and xt (i.e., estimte a and b)
(2) Incorporate residuals in a short run model:
DF: Delta(ut) = au + bu*u(t-1) + error
ADF: Delta(ut) = au + bu*u(t-1) + (lags of Delta ut) error
Use special tabulated critical values to test whether bu /= 0. If true, conclude that the residuals
are stationary and therefore x and y are cointegrated. If we fail to reject that bu = 0, conclude
that x and y are not cointegrated.
Consider two stocks: AAAPL, and MSFT. We want to see whether they are cointegrated. Treat AAPL = y
and MSFT = x:.
MSFT = (23.86, 20.89, 20.13, 18.25, 16.05, 16.88, 19.19, 19.96, 21.89, 26.16);
AAPL = (141.97,135.81,125.83, 105.12, 89.31, 90.13,85.35,92.67,107.59,113.66);