A looser cointegration concept using fractional integration parameters and quantification of market responsiveness

Many economic variables are fractionally integrated of order d, FI(d) with unequal d's. For modeling their long-run equilibria, we explain why the usual cointegration fails to exist and the unit root type tests have low power. Hence, we propose a looser concept called "tie integration". A new numerical minimization problem reveals the value of d in the absence of tie integration, denoted by d(null). We use the d from residuals of a regression, as well as, d(null) to devise a new index called strength of tie (SOT). An application quantifies market responsiveness. (C) 2002 Elsevier Science B.V. All rights reserved.