A flexible functional-circular regression model for analyzing temperature curves

TL;DR

This paper introduces a novel nonparametric regression model for analyzing temperature curves as functional covariates with circular responses, aiding climate change assessment.

Contribution

It develops a flexible Nadaraya-Watson-type estimator for functional covariate and circular response, with theoretical properties and practical evaluation.

Findings

Estimator's asymptotic bias and variance derived

Simulation study confirms finite sample performance

Applied to real temperature data revealing climate patterns

Abstract

Changes on temperature patterns, on a local scale, are perceived by individuals as the most direct indicators of global warming and climate change. As a specific example, for an Atlantic climate location, spring and fall seasons should present a mild transition between winter and summer, and summer and winter, respectively. By observing daily temperature curves along time, being each curve attached to a certain calendar day, a regression model for these variables (temperature curve as covariate and calendar day as response) would be useful for modeling their relation for a certain period. In addition, temperature changes could be assessed by prediction and observation comparisons in the long run. Such a model is presented and studied in this work, considering a nonparametric Nadaraya-Watson-type estimator for functional covariate and circular response. The asymptotic bias and variance of this estimator, as well as its asymptotic distribution are derived. Its finite sample performance is evaluated in a simulation study and the proposal is applied to investigate a real-data set concerning temperature curves.