Testing for Trends in High-Dimensional Time Series

• Activity Number: 477 - Complex Time Series Analysis
• Type: Invited
• Date/Time: Wednesday, July 31, 2019 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Likai Chen* and Wei Biao Wu
• Companies: Washington University in Saint Louis and University of Chicago
• Keywords: Asymptotic normality; Gaussian multiplier testing procedure; Temporal and spatial dependence; Parametric testing

Abstract

We consider statistical inference for trends of high-dimensional time series. Based on a modified ?2 distance between parametric and nonparametric trend estimators, we propose a de-diagonalized quadratic form test statistic for testing patterns on trends, such as linear, quadratic, or parallel forms. We develop an asymptotic theory for the test statistic. A Gaussian multiplier testing procedure is proposed and it has an improved finite sample performance. Our testing procedure is applied to a spatial temporal temperature data gathered from various locations across America. A simulation study is also presented to illustrate the performance of our testing method.