Log prices (adjusted for dividends, splits etc.) of US equity Duke Energy (DUK) were regressed against those of US equity Goldman Sachs (GS) (a bank); the residuals were then regressed on lagged residuals which gave a coefficient estimate of 0.973 with an estimated standard error of 0.024.
a) Use this information to compute an Engle-Granger cointegration test statistic.
b) Do you accept or reject cointegration between DUK and GS at 5% significance based on this test?
c) Is cointegration associated with stationary or non-stationary residuals from a regression like DUK vs. GS?
d) What are some risks in using statistical arbitrage to trade stocks in different industries that you might worry about?