Abstract

Inference of mean structure is an important problem in time series analysis. Various tests have been developed to test for different mean structures, for example, the presence of structural breaks, and parametric mean structures. However, many of them are designed for handling specific mean structures, and may lose power upon violation of such structural assumptions. In this paper, we propose a new mean stationarity test built around the signal variance. The proposed test is based on a super-efficient estimator which could achieve a convergence rate faster than $\sqrt{n}$.

It can detect non-constancy of the mean function under serial dependence. It is shown to have promising power, especially in detecting hardly noticeable oscillating structures. The proposal is further generalized to test for smooth trend structures and relative signal variability.

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