2019/04/09 by Bibinger, Markus
#60G22 #62M10 #FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1904.04556
In this letter, we construct cusum change-point tests for the Hurst exponent and the volatility of a discretely observed fractional Brownian motion. As a statistical application of the functional Breuer-Major theorems by Bégyn (2007) and Nourdin and Nualart (2019), we show under infill asymptotics consistency of the tests and weak convergence to the Kolmogorov-Smirnov law under the no-change hypothesis. The test is feasible and pivotal in the sense that it is based on a statistic and critical values which do not require knowledge of any parameter values. Consistent estimation of the break date under the alternative hypothesis is established. We demonstrate the finite-sample properties in simulations and a data example.