We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the linear ARCH model. Contrary to existing literature we allow the parameters to be in the region where no stationary version of the process exists

It is a well-established fact that testing a null hypothesis on the boundary of the parameter space, with an unknown number of nuisance parameters at the boundary, is infeasible in practice in the sense that limiting distributions of standard test statistics are non-pivotal. In particular,...

This paper develops tests for the correct specification of the conditional variance function in GARCH models when the true parameter may lie on the boundary of the parameter space. The test statistics considered are of Kolmogorov-Smirnov and Cramér-von Mises type, and are based on a certain...

This paper considers asymptotic inference in the multivariate BEKK model based on (co-)variance targeting (VT). By de finition the VT estimator is a two-step estimator and the theory presented is based on expansions of the modifi ed likelihood function, or estimating function, corresponding to...

We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time...