We propose a modified version of the nonparametric level crossing random walk test, in which the crossing level is determined locally. This modification results in a test that is robust to unknown multiple structural breaks in the level and slope of the trend function under both the null and alternative hypothesis. No knowledge regarding the number or timing of the breaks is required. A bootstrap method is suggested to select the extent of the localization in order to maximize power in a proximate model. To control overall test size we propose a second outer bootstrap, in which we replicate the entire procedure, including the inner bootstrap used to select the localization parameter. The test is applied to Canadian nominal inflation and nominal interest rate series with implications for the Fisher hypothesis.
Key words: Level crossing, random walk, structural breaks, unit root, robustness.
JEL: C12, C14, C22