Past, Present and Future of Testing for Nonlinearity in Time Series

Ali Habibnia
Working Paper

However, many real-world phenomena and series are nonlinear in nature, a common assumption that is often made in time series analysis is that the series conforms to a linear model. In this paper, we provide a comparative review of the past and recent advances in statistical tests for testing the notion of time series linearity. In addition, we examine, via simulated series, the performance of the major nonlinearity tests to highlight their assets and limitations and to identify future directions in this multidisciplinary research area. In the paper, we first discuss the definition and the characteristics of (non)linear processes and then we present a tentative classification of the various tests and approaches that have been proposed in the literature, shared among different disciplines, such as Statistics, Physics, Econometrics, Nonlinear Dynamics, and Engineering. The main idea behind various nonlinearity tests is a hypothesis testing procedure. Therefore, we discuss different null hypotheses and test statistics. We also briefly cover statistical approaches that can be used to detect nonlinear dependencies between the multivariate time series. Finally, we investigate nonlinear features of real financial time series, including … We briefly discuss the implication of nonlinearity tests for model selection and forecasting. We show that the forecasting technique arises as a natural extension of, and as a complement to, existing nonlinearity tests.

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