A Transaction-Level Pure-Jump Model Yielding Cointegration

A contemporaneous linear combination of two or more time series is less persistent than the individual series. Engle and Granger (1987) allowed for both standard and fractional cointegration. Under standard cointegration, the memory parameter is reduced from 1 to 0, while under fractional cointegration the level of reduction need not be an integer thus is more general. Empirical examples include: interest rates of different horizons, implied versus realized volatility, pairs trading strategy, etc. – p.