Tests for an Autoregressive Unit Root in the Variables of the Overshooting Model

Abstract

In this section, a test of an autoregressive unit root by Elliott, Rothenberg, and Stock (1992) will be performed with respect to the variables in equation (4) from section B. The tests of an autoregressive unit root are necessary in order to decide whether a cointegration analysis is useful. If all variables were I(0) processes, the effort to specify an error correction model would not be necessary and “classical” methods could be applied. The tests of unit roots will also show which of the real exchange rates are I(1) or I(0) processes. The time series properties of real exchange rates are important to know for foreign exchange rate modelling. To model real exchange rates correctly their stochastic properties should be known. The results of these tests will also decide which error correction model should be used. For example, if several variables turn out to be trend-stationary, an error correction model (ECM) should be applied which allows for this kind of variables or more precisely which allows for stochastic cointegration^l.

Article Footnote

^lOgaki and Park (1990) coined this term.