Analyzing the Role of Nonstationarity in Time Series Data and Its Effect on Forecasting Accuracy

Posted: Mar 22, 2023

• Olivia Thompson
• Victoria Lewis
• Samuel Lee

Abstract

Time series forecasting represents a cornerstone of analytical methodology across numerous disciplines, from economics and finance to environmental science and engineering. The fundamental assumption underlying many traditional forecasting techniques is that of stationarity, wherein the statistical properties of the time series remain constant over time. However, real-world data frequently violate this assumption, exhibiting various forms of nonstationarity that complicate forecasting efforts and challenge conventional analytical frameworks. The prevailing approach to handling nonstationarity has largely centered on transformation techniques, primarily differencing, to achieve stationarity before applying forecasting models. This oversimplified treatment fails to capture the rich diversity of nonstationary behaviors and their differential impacts on forecasting performance. Our research addresses critical gaps in the current understanding of nonstationarity by proposing a multidimensional characterization framework that distinguishes between structural breaks, time-varying variance, and evolving frequency components. We contend that these distinct forms of nonstationarity influence forecasting accuracy through different mechanisms and therefore require tailored methodological approaches. The conventional practice of treating nonstationarity as a monolithic phenomenon to be eliminated through differencing overlooks valuable information embedded in the nonstationary structure of the data. This investigation was motivated by three fundamental research questions that remain inadequately addressed in the existing literature. First, how do different types of nonstationarity manifest in real-world time series data across various domains? Second, what are the specific mechanisms through which each type