To detect a changed segment (so called epidemic changes) in a time series, variants of the CUSUM statistic are frequently used. However, they are sensitive to outliers in the data and do not perform well for heavy tailed data, especially when short segments get a high weight in the test...

Let {Xk:k≥1} be a linear process with values in the separable Hilbert space L2(μ) given by Xk=∑j=0∞(j+1)−Dεk−j for each k≥1, where D is defined by Df={d(s)f(s):s∈S} for each f∈L2(μ) with d:S→R and {εk:k∈Z} are independent and identically distributed L2(μ)-valued random...