A0624
Title: Nonlinear vector autoregressive models and unit roots
Authors: Rickard Sandberg - Stockholm School of Economics (Sweden) [presenting]
Abstract: The purpose is to investigate the challenges of testing for linearity in the context of univariate and multivariate smooth transition autoregressive (STAR and VSTAR) models. A key focus is the impact of unit root processes on the distribution of linearity test statistics, which can lead to substantial size distortions. These distortions pose a risk of spurious rejections of linearity, potentially resulting in model misspecification and unreliable inference. For example, a test nominally set at the 5\% significance level may exhibit empirical rejection rates as high as 17.1\% in univariate STAR models and 22.6\% in bivariate VSTAR models. Critically, these distortions are shown to magnify with the dimensionality of the system; in a VSTAR model with four variables, the empirical size reaches 46.1\%. A novel contribution is the derivation of the asymptotic distributions of linearity tests under a unit root assumption in multivariate systems - an extension not previously addressed in the literature. An empirical application using U.S. inflation and Federal Funds Rate data illustrates the importance of accounting for unit roots prior to testing for nonlinearity. The findings emphasize the need for adjusted critical values and robust testing strategies when working with persistent and high-dimensional macroeconomic time series.
