The Lawrence-Lewis Pareto process: an extremal approach

Pareto processes are more suitable for time series with heavy tailed marginals than the classical gaussian. Here we consider the Lawrence-Lewis Pareto process. In particular, we analyze long-range and local dependence and compute some extremal measures. This will provide us some more diagnostic tools and new estimators for the autoregressive parameter of the process. Based on a simulation study we will see that the new methods may be good alternatives in what concerns robustness.