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Title: Simultaneous inference for time series functional linear regression Authors:  Yan Cui - Harbin Institute of Technology (China)
Zhou Zhou - The Chinese University of Hong Kong (China) [presenting]
Abstract: The focus is on the problem of joint simultaneous confidence band (JSCB) construction for regression coefficient functions of time series scalar-on-function linear regression when the regression model is estimated by a roughness penalization approach with flexible choices of orthonormal basis functions. A simple and unified multiplier bootstrap methodology is proposed for the JSCB construction, which is shown to achieve the correct coverage probability asymptotically. Furthermore, the JSCB is asymptotically robust to inconsistently estimated standard deviations of the model. The proposed methodology is applied to a time series data set of the electricity market to visually investigate and formally test the overall regression relationship as well as perform model validation. A uniform Gaussian approximation and comparison result overall Euclidean convex sets for normalized sums of a class of moderately high-dimensional stationary time series is established.