In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model which is the foundation to initiate the theoretical...

We develop a uniform test for detecting and dating the integrated or mildly explosive behaviour of a strictly stationary generalized autoregressive conditional heteroskedasticity (GARCH) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters...

We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH(r, s) (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative...

For multiple change-points detection of high-dimensional time series, we provide asymptotic theory concerning the consistency and the asymptotic distribution of the breakpoint statistics and estimated break sizes. The theory backs up a simple two- step procedure for detecting and estimating...

We consider a new procedure for detecting structural breaks in mean for high- dimensional time series. We target breaks happening at unknown time points and locations. In particular, at a fixed time point our method is concerned with either the biggest break in one location or aggregating...

The paper presents a systematic theory for asymptotic inferences based on autocovariances of stationary processes. We consider nonparametric tests for se rial correlations using the maximum and the quadratic deviations of sample autocovariances. For these cases, with proper centering and...