This paper proposes residual-based tests for cointegration with three-regime threshold autoregressive (TAR) adjustment. We propose Wald-type and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>t</mi> </math> </EquationSource> </InlineEquation>-type tests that have the null hypothesis of linear no cointegration and the alternative of cointegration with three-regime TAR adjustment...</equationsource></equationsource></inlineequation>

Testing for cointegration in the presence of nonlinear adjustments or structural breaks is important for examining the equilibrium relationship among economic variables. It is known that standard cointegration tests perform poorly when a cointegration relationship has nonlinear adjustments or...