Simultaneous Inference for Time Series Functional Linear Regression

TL;DR

This paper introduces a bootstrap-based method for constructing simultaneous confidence bands for regression functions in time series scalar-on-function linear regression, ensuring accurate coverage and robustness.

Contribution

It proposes a unified multiplier bootstrap approach for JSCB construction that is asymptotically valid and robust to standard deviation estimation issues.

Findings

The methodology achieves correct asymptotic coverage probability.

It is robust to inconsistent standard deviation estimates.

Applied to electricity market data for regression analysis and validation.

Abstract

We consider 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 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 electricity market to visually investigate and formally test the overall regression relationship as well as perform model validation.