Modelling Cointegrated I(2) Systems with an Application to Money and Exchange Rates

Abstract

In an introductory chapter we collect together some recent results on the representation, estimation and testing of cointegrated I(2) systems. In particular, we focus on some recent developments such as tests on the cointegration parameters of Kongsted [1998, 2000] and examining in detail the influence of deterministic components in the I(2) model as well as providing an overview of the maximum likelihood procedure detailed in Johansen [1997].

The first empirical chapter provides evidence on a range of issues concerning the correct treatment of I(2) variables when modelling UK money demand. We show that by including the dummy variables in Hendry and Mizon [1993] the conclusions on the number of cointegrating relations and I(2) trends arrived at in Johansen [1992], Paruolo [1996] and Rahbek et al. [1999] are unchanged. However, we also show that the real transformation employed in Hendry and Mizon [1993] and Hendry and Doornik [1994] is inadequate to reduce the model to I(1) space and, moreover, that the common result of weak exogeneity with respect to the cointegration parameters may also rest upon this improper restriction. Instead, we show that by correctly accounting for the time series properties of the data a congruent equilibrium correction model can be obtained that incorporates the long run information in the model. Furthermore, we show that this model provides superior forecasting performance when compared to simple time series models such as a vector autoregression in double differences.

The second empirical chapter provides the first empirical examination of the monetary exchange rate model that allows for the presence of I(2) variables in the data. First, for the dollar-sterling exchange rate over the modern float we find strong support for the existence of cointegration among the variables in the monetary model. In addition, by testing for the number of I(1) and I(2) trends we find evidence for I(2) variables in the data. As a consequence the stationary cointegrating relation found corresponds to a polynomial relation where the linear combination of the differences of the variables are required in order to provide a stationary relationship.

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