We develop new multiscale methods to test qualitative hypotheses about the function m in the non-parametric regression model Yt,T=m(t/T)+ɛt with time series errors ɛt. In time series applications, m represents a non-parametric time trend. Practitioners are often interested in whether the trend...

The present paper is devoted to the study of the hybrids of empirical and partial sums processes. In the first part, we present a synthesis of results related to these processes and their connection with the empirical and compound process. We obtain new results on the precise asymptotics in the...

We improve, first, a strong invariance principle from Kifer (2013) [10] for nonconventional sums of the form ∑n=1[Nt]F(X(n),X(2n),…,X(ℓn)) (normalized by 1/N) where X(n),n≥0’s is a sufficiently fast mixing vector process with some moment conditions and stationarity properties and F...

Sequential tests that are generalizations of Page's CUSUM tests are proposed for detecting an abrupt change in any parameter, or in any collection of parameters of an autoregressive time series model. These tests accommodate nuisance parameters. They are based on large sample approximations to...