Stability conditions for a bivariate arch system which is cointegrated in mean

This note gives necessary and sufficient conditions for covariance stationarity in a bivariate system of individually first-order integrated (i.e. difference-stationary) processes. The two processes are linked by a cointegrating relation and by a special ARCH model that describes their time-changing volatility. The problem of deriving necessary conditions for strict stationarity in this system is demonstrated using Monte Carlo simulation. The conditions of the theorem are highlighted using empirical examples.