Measuring the Degree of Distribution Changes Under Local Stationarity

ABSTRACT The present article introduces new methods for quantifying how intensively the distribution changes over time in a quite general locally stationary framework. Concretely, two characteristic function‐based measures for quantifying the intensity of distribution changes are introduced and estimated. By combining these estimators with suitable dependent wild bootstrap procedures, confidence bands for both measures are estimated. The coverage ratios of the estimated confidence intervals are investigated for finite sample sizes by using simulation studies. As applications, the distribution change intensity of the log returns corresponding to several stocks in chosen time periods is investigated.