Testing for Sign and Amplitude Asymmetries Using Threshold Autoregressions

This paper uses threshold autoregressions to characterize asymmetries in adjustment dynamics and develops likelihood ratio tests to detect them. A robust bootstrap technique is proposed to circumvent the problem that the asymptotic distribution of the test statistics is non-standard. Monte Carlo simulations show that the bootstrap tests are correctly sized and are robust to near-unit roots and non-Gaussian errors. Their power is reasonable, improves sharply with the time series length and remains satisfactory for smooth transition autoregressions. Our approach combined with nonparametric tests can discriminate between asymmetries in adjustment dynamics and in innovations. An application to four monthly US dollar spot returns provides evidence of amplitude asymmetry