Records Properties of Non Stationary Time Series

This article compares the statistical properties of the records from independent and identically distributed time series with those of time series containing a single unit root. It is shown that there are important differences in both the limiting distributions and the convergence rates of the associated record counting processes. Since the record properties of independent and identically distributed time series are shared by a large class of stationary time series, the reported differences underline the possibility of using record-based statistics for robust testing procedures of the unit root hypothesis. We make an extension of the nonparametric test for the Range Unit Root test (RUR) proposed in Aparicio et al. (2006). We prove some properties for the test statistic in the context of the renewal theory and we suggest two new candidates to test the hypothesis of random walk with positive and negative drift.