Extremal clustering in non-stationary random sequences

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but identically distributed sequences of random variables subject to suitable long range dependence restrictions. We find that the limiting distribution of appropriately normalized sample maxima depends on a parameter that measures the average extremal clustering of the sequence. Based on this new representation we derive the asymptotic distribution for the time between consecutive extreme observations and construct moment and likelihood based estimators for measures of extremal clustering. We specialize our results to random sequences with periodic dependence structure.

On the strong attraction of functions on dependent variables to the normal law

For symmetric functions on random variables from stationary sequences satisfying the uniformly strong mixing condition, the general conditions of attraction to the normal law in terms of distributions of individual items are obtained. The main result of the paper generalizes all known to present results of this type.

Central limit theorems for nearly long range dependent subordinated linear processes

The limit behavior of partial sums for short range dependent stationary sequences (with summable autocovariances) and for long range dependent sequences (with autocovariances summing up to infinity) differs in various aspects. We prove central limit theorems for partial sums of subordinated linear processes of arbitrary power rank which are at the border of short and long range dependence.