Testing Normality of Functional Time Series
针对函数型时间序列数据，提出了基于Jarque-Bera检验的正态性检验方法，解决了未知时间依赖结构和最优投影空间估计两大难题，并通过污染数据和日内价格曲线验证了方法的有效性。
We develop tests of normality for time series of functions. The tests are related to the commonly used Jarque–Bera test. The assumption of normality has played an important role in many methodological and theoretical developments in the field of functional data analysis. Yet, no inferential procedures to verify it have been proposed so far, even for i.i.d. functions. We propose several approaches which handle two paramount challenges: (i) the unknown temporal dependence structure and (ii) the estimation of the optimal finite‐dimensional projection space. We evaluate the tests via simulations and establish their large sample validity under general conditions. We obtain useful insights by applying them to pollution and intraday price curves. While the pollution curves can be treated as normal, the normality of high‐frequency price curves is rejected.