In this paper, we propose a modified CUSUM of squares test in time series regression models with a non-stationary regressor and show that the limiting distribution of this test is the sup of the absolute value of a Brownian bridge.

In this paper, we consider the monitoring process in time series regression models with nonstationary regressors. To this end, we propose a monitoring process based on a modified square of residuals. Simulation results are provided for illustration.

This paper proposes a quantile regression estimator for the diffusion parameter in diffusion processes with compound Poisson jumps. The method is based on discretely sampled observations at high frequency. We verify its consistency and exhibit its robustness to jumps through a simulation study.

In this paper, we study the Jarque-Bera test for the normality of the innovations of multivariate GARCH models. It is shown that the test is distribution free and its limiting null distribution is a chi-square distribution.