Nonlinear cointegration: Theory and Application to Purchasing Power Parity
نویسندگان
چکیده
In this paper, we study a smooth-transition type of nonlinear cointegration among a dynamic system, in which the proposed definition nests Engle and Granger (1987)’s linear cointegration. Based on the Smooth Transition Autoregressive (STAR) models, a triangular representation for the nonlinearly cointegrated system is introduced. Furthermore, two tests for nonlinear cointegration are derived in this paper: one is a residual-based test for testing the null hypothesis of no nonlinear cointegration and the other is a test for testing the hypothesis of linear cointegration against nonlinear cointegration. The statistical properties of the second test are investigated. An empirical example is illustrated by applying the first testing procedure to the dollar/lira real exchange rate. It is found that there is no linear cointegration but a nonlinearly cointegrating relation in the investigated purchasing power parity (PPP). The PPP puzzle in Hamilton (1994) can be solved by applying our nonlinear cointegration.
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Testing for linear cointegration against nonlinear cointegration: Theory and application to Purchasing power parity
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