Variance targeting estimation (VTE) is a technique used to alleviate the numerical difficulties encountered in the quasi-maximum likelihood estimation (QMLE) of GARCH models. It relies on a reparameterization of the model and a first-step estimation of the unconditional variance. The remaining...

A common goal in modeling and data mining is to determine, based on sample data, whether or not a change of some sort has occurred in a quantity of interest. The study of statistical problems of this nature is typically referred to as change point analysis. Though change point analysis...

We propose a nonparametric estimator for the rate of spread of an introduced population. We prove that the limit distribution of the estimator is normal or stable, depending on the behavior of the moment generating function. We show that resampling methods can also be used to approximate the...

We propose a test for a change in the parameters of a GARCH(p,q) model. The test is based on approximate likelihood scores and does not require the observations to have finite variance. We show that the test has asymptotically correct size under weak assumptions on model errors.

We find necessary and sufficient conditions for the almost sure finiteness of weighted integrals of stable processes with parameters [alpha] = 1 and [beta] [not equal to] 0.

This note represents a probability inequality for an approximation of Abel sums of independent, identically distributed random variables. This approximation implies a rate for the Prohorov-Lévy distance between Abel sums and their limit process.

Strong approximations of sums of random vectors indexed by a renewal process are presented. The method is to derive these approximations of generalized renewal processes from the already existing or future approximations of associated partial sums. Consequences of the main theorem are a...

We establish best possible rates for approximating random walk local time by Brownian local time.

We connect the rate of consistency of the quasi-maximum likelihood estimator in GARCH(p,q) sequences with the number of the moments of the innovations.