A new method for detecting regime switches between different probability distributions in financial time series is shown. In the proposed method, time series observations are divided into several segments, and a Gaussian model or a Cauchy model is fitted to each segment. The goodness of fit of...

Let Z(τ,t) is the number of individuals at time τ having more than θ(t−τ) descendants at time t,tτ. Here θ(t) is some non-negative function. Limit distributions for Z(τ,t) when population evolves according to critical branching processes with time homogeneous immigration and...