Nested functional ANOVA with pointwise and global inference: theory and application to COVID-Era financial data

We propose a nested functional analysis of variance (FANOVA) model to investigate hierarchical variation structures in functional data. The model extends classical ANOVA by incorporating both main effects and nested subgroup effects, allowing for the decomposition of functional variation across multiple levels. Model parameters are estimated using matrix-based representations under functional linear model assumptions. For hypothesis testing, we develop pointwise F-type statistics and global tests based on the $L^2$ norm of the effect functions, with null distributions approximated via Welch-Satterthwaite techniques. Through extensive simulation studies, we assess the accuracy of parameter estimation, control of Type I error, and power under various noise levels, sample sizes, and contamination scenarios. The methodology is further illustrated through an application to stock market index data from 24 countries during the COVID-19 pandemic, where we analyze regional and nested economic effects. The results demonstrate that the proposed nested FANOVA framework effectively captures structured functional variation and remains robust under a range of realistic data conditions.