Online bootstrap monitoring of the stationarity for a class of heavy tailed random signals

Impulse noise makes random signals occur heavy tails. For the online heavy tailed random signal with symmetrically distributed stable noise, we propose a kernel weighted variance ratio procedure to sequentially detect its stationarity. The asymptotic distribution of the monitoring statistic under nonstationary null hypothesis is derived, and its consistency is proved. In order to determine the critical values of the monitoring statistic and avoid the estimation of the tail index, we propose a bootstrap resampling method. Simulations and analysis of two groups of real data validate the proposed procedure.