SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

Abstract: In this paper two simple tests to distinguish between unit root processes and stationary nonlinear processes are proposed. New limit distribution results are provided, together with two F type test statistics for the joint unit root and linearity hypothesis against a specific nonlinear alternative. Nonlinearity is defined through the smooth transition autoregressive model. Due to occasional size distortion in small samples, a simple bootstrap method is proposed for estimating the p-values of the tests. Power simulations show that the two proposed tests have at least the same or higher power than the corresponding Dickey-Fuller tests. Finally, as an example, the tests are applied on the seasonally adjusted U.S. monthly unemployment rate. The linear unit root hypothesis is strongly rejected, showing considerable evidence that the series is better described by a stationary smooth transition autoregressive process than a random walk.

Keywords: Smooth transition autoregressive model; nonlinearity; unit root; Brownian motion; critical values; bootstrap; Monte Carlo simulations; unemployment rate

JEL-codes: C22; C52

24 pages, November 28, 2003

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