Testing for Trends in High-Dimensional Time Series

Abstract: This talk considers statistical inference for trends of high-dimensional time series. Based on a modified $\mathcal{L}^2$ 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.

Host: Jose Figueroa-Lopez