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Title: Detecting relevant changes in the mean of non-stationary processes: A mass excess approach Authors:  Holger Dette - Ruhr-Universitaet Bochum (Germany)
Weichi Wu - Ruhr University Bochum (Germany) [presenting]
Abstract: The focus in on the problem of testing if a sequence of means $(\mu_t)_{t =1,\ldots ,n }$ of a non-stationary time series $(X_t)_{t =1,\ldots ,n }$ is stable in the sense that the difference of the means $\mu_1$ and $\mu_t$ between the initial time $t=1$ and any other time is smaller than a given threshold, that is $ | \mu_1 - \mu_t | \leq c $ for all $t =1,\ldots ,n $. A test for hypotheses of this type is developed using a bias corrected monotone rearranged local estimator and asymptotic normality of the corresponding test statistic is established. As the asymptotic variance depends on the location of the critical roots of the equation $| \mu_1 - \mu_t | = c$, a new bootstrap procedure is proposed to obtain critical values and its consistency is established. As a consequence, we are able to quantitatively describe relevant deviations of a non-stationary sequence from its initial value. The results are illustrated by means of a simulation study and by analyzing data examples.