Testing for Nonlinearity in Mean in the Presence of Heteroskedasticity

Abstract

This paper considers an important practical problem in testing time-series data for nonlinearity in mean. Most popular tests reject the null hypothesis of linearity too frequently if the the data are heteroskedastic. Two approaches to redressing this size distortion are considered, both of which have been proposed previously in the literature although not in relation to this particular problem. These are the heteroskedasticityrobust-auxiliary-regression approach and the wild bootstrap. Simulation results indicate that both approaches are e¤ective in reducing the size distortion and that the wild bootstrap o¤ers better performance in smaller samples. Two practical examples are then used to illustrate the procedures and demonstrate the potential pitfalls encountered when using non-robust tests.Keywords nonlinearity in mean, heteroskedasticity, wild bootstrap, empirical size and power JEL Classi…cation C12, C22, C52

Weighted Smooth Transition Regressions

“…Further, we advocate the use of the wild bootstrap to account for possible heteroskedasticity of unknown form. In line with Becker and Hurn (2009), our results indicate that the wild bootstrap approach performs very well, delivering reliable finite sample size and power comparable to that achieved by tests that assume homoskedasticity when the true data‐generating process (DGP) is homoskedastic.…”

Non‐linearities in the relation between the exchange rate and its fundamentals

“…As suggested in Lee et al (1993), Hurn (2004) and Becker and Hurn (2006), when timeseries are heteroskedastic, which is often the case in exchange rate modelling, usual tests employed to detect non-linearity might produce misleading results. In particular, these tests tend to over reject the null of linearity.…”

“…In particular, these tests tend to over reject the null of linearity. In order to control for the size distortion eventually arising from non-constant variance in selected time-series we compute a different version of the Ramsey test based on the heteroskedasticity-consistent regression as suggested in Becker and Hurn (2006). The results are shown in the last column of Table 3.…”

A Time Series Analysis of U.K. Construction and Real Estate Indices

“…On the one hand, we compute the Kaplan's (1994) test and, on the other hand, we compute Terasvirta et al (1993) test with wild bootstrap as suggested by Becker and Hurn (2004). We compute two tests because, as argued by Barnett el al.…”

“…To account for conditional heteroskedasticity, we apply a fixed-design wild bootstrap (WB) approach, following Becker and Hurn's (2004) suggestion and Davidson and Flachaire's (2000) WB procedure, as follows:…”