Fourier Regression Analysis: An Introduction and Application to Model City-level Climate Emissions

Abstract

This paper introduces a novel regression method that uses a Fourier series basis to incorporate trigonometric terms when modeling data. Fourier series are a powerful tool used widely in other disciplines but are, to our knowledge, rarely used in the social sciences if at all. Using a Monte Carlo simulation with known model parameters, we demonstrate that intercept and slope estimates of traditional polynomial regression methods and moving averages are biased when the underlying data is periodic with implications for causal inference, especially for regression discontinuity (RD) and interrupted time series (ITS) approaches. We then apply Fourier regressions to real world emissions data from local administrative units (LAUs) that participate in the European Union Covenant of Mayors (EUCoM)-the largest transnational climate initiative in Europe-as an example of how this approach can improve estimation of performance trends compared to traditional regression methods.

Keywords: Fourier, Monte Carlo, interrupted time series, regression discontinuity, emissions, climate change, Covenant of Mayors

JEL Classification: C22, C51