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.

翻译：我们考虑了在以粗糙惩罚方法估算回归模型并灵活选择正态基本功能时,同时为时序卡路里-功能线性回归回归的回归系数函数进行联合同时构建信任带(JSCB)的问题,为JSCB构建提出了简单和统一的乘数陷阱方法,该方法显示,该模型的准确覆盖概率是暂时的;此外,JSCB对于该模型的标准偏差估算不一致,也几乎是站不住脚的,拟议方法适用于电力市场的时间序列数据集,以便目视调查和正式测试总体回归关系,并进行模型验证。