Testing for Smooth Transition Nonlinearity in the Presence of Outliers

Abstract

Regime-switching models, like the smooth transition autoregressive [STAR] model, are typically applied to time series of moderate length. Hence, the nonlinear features that these models intend to describe may be reflected in only a few observations. Conversely, neglected outliers in a linear time series of moderate length may incorrectly suggest STAR (or other) type(s of) nonlinearity. In this article we propose outlier robust tests for STAR-type nonlinearity. These tests are designed such that they have a better level and power behavior than standard nonrobust tests in situations with outliers. We formally derive local and global robustness properties of the new tests. Extensive Monte Carlo simulations show the practical usefulness of the robust tests. An application to several quarterly industrial production indexes illustrates that apparent nonlinearity in time series sometimes seems due to only a few outliers.

KEY WORDS:

• Asymptotic theory
• Influence function
• Lagrange multiplier-type tests
• Monte Carlo simulation
• Robust estimation