Advances in estimation and inference for historical functional linear models

Abstract

AbstractHistorical functional linear models or HFLMs are a class of function‐on‐function regression models that seek to restrict the relationship between two or more time‐dependent functions, or curves, of data where one function is a natural outcome and the others are natural predictors. A natural predictor is a predictor that occurs in time before, or at most concurrently with, an outcome. The primary challenge in developing methods for HFLMs is ensuring that the time‐dependent relationship between the outcome and predictors is enforced and that no “unnatural” relationships are allowed, for example, where estimation, inference, or prediction are conducted on or using coefficients such that the outcome occurs before the predictor. A number of authors consider a variety of modeling frameworks for HFLMs. This work seeks to introduce the basic HFLM, explore the various approaches for its estimation, and discuss recent advances.This article is categorized under: Statistical Models > Linear Models Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Models > Model Selection