It is known that the tail index of a GARCH model is determined by a moment equation, which involves the underlying unknown parameters of the model. A tail index estimator can therefore be constructed by solving the sample moment equation with the unknown parameters being replaced by its...

Researchers in actuarial sciences have investigated the tail behavior of the LCR and ECOMOR reinsurance treaties separately for managing extreme risks in reinsurance business. In practice, a reinsurance company may possess these two treaties simultaneously. Therefore, investigating the joint...

An empirical likelihood–based confidence interval is proposed for interval estimations of the autoregressive coefficient of a first-order autoregressive model via weighted score equations. Although the proposed weighted estimate is less efficient than the usual least squares estimate, its...

In certain cases partial sums of i.i.d. random variables with finite variance are better approximated by asequence of stable distributions with indices alpha_n o 2 than by a normal distribution. We discusswhen this happens and how much the convergence rate can be improved by using...

Suppose our data {Xn} come from the model Xt=[summation operator]j=0[infinity]cjZt-j, where {Zn} are i.i.d. with a symmetric distribution function which lies in the domain of normal attraction of a stable law with index [alpha][set membership, variant](1,2). Further we assume that cj=jd-1L(j),...