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This paper consider tests for LSTAR models accommodating multiple time dependent transitions between regimes when the data generating process is non-stationary. The asymptotic null distribution of the tests, in contrast to the normality results in Lin and Teräsvirta (1994) , are non-standard. The tests show upon modest size distortions, and the power in LSTAR models with multiple transitions is very satisfactory. The tests are applied to Swedish unemployment rates and the hysteresis hypothesisdoi:10.1080/07474938.2011.607085 fatcat:b25oj56ju5a45b4r24ujtrx4py