Non-Stationarity in Time-Series Analysis: Modeling Stochastic and Deterministic Trends

Abstract

Time series analysis is increasingly popular across scientific domains. A key concept in time series analysis is stationarity, the stability of statistical properties of a time series. Understanding stationarity is crucial to addressing frequent issues in time series analysis such as the consequences of failing to model non-stationarity, how to determine the mechanisms generating non-stationarity, and consequently how to model those mechanisms (i.e., by differencing or detrending). However, many empirical researchers have a limited understanding of stationarity, which can lead to the use of incorrect research practices and misleading substantive conclusions. In this paper, we address this problem by answering these questions in an accessible way. To this end, we study how researchers can use detrending and differencing to model trends in time series analysis. We show via simulation the consequences of modeling trends inappropriately, and evaluate the performance of one popular approach to distinguish different trend types in empirical data. We present these results in an accessible way, providing an extensive introduction to key concepts in time series analysis, illustrated throughout with simple examples. Finally, we discuss a number of take-home messages and extensions to standard approaches, which directly address more complex time-series analysis problems encountered by empirical researchers.