Localized level crossing random walk test robust to the presence of structural breaks

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. An algorithm is proposed to select the degree of localization in order to maximize bootstrapped power in a proximate model. A computational procedure is then developed to adjust the critical values for the effect of this selection procedure by replicating it under the null hypothesis. The test is applied to Canadian nominal inflation and nominal interest rate series with implications for the Fisher hypothesis. Keyword: Level crossing, random walk, structural breaks, unit root, robustness.