Time-Varying Correlation for Noncentered Nonstationary Time Series: Simultaneous Inference and Visualization
Ting Zhang, Yu Shao · Statistica Sinica · 2023
We consider simultaneous inference of the time-varying correlation as a function of time between two nonstationary time series when their trend functions are unknown.Unlike the stationary setting where the effect of precentering using the sample mean is trivially negligible, in the nonstationary setting it is difficult to quantify the impact from precentering using nonparametric trend function estimators.This is mainly due to the trend estimators being time-varying across different time points, which makes it difficult to quantify their cumulative interaction with the error process in the time series setting.We propose to fix this unpleasant issue by using a centering scheme that, instead of aligning with the time point at which the data is observed, aligns with the time point at which the local correlation estimation is performed.We show that this new centering scheme can lead to simultaneous confidence bands with a solid theoretical guarantee for the time-varying correlation between two nonstationary time series Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) when their trend functions are unknown.Numerical examples including a real data analysis are provided to illustrate the proposed method.