Testing linearity against smooth transition autoregression using a parametric bootstrap

When testing the null hypothesis of linearity of a univariate time series against smooth transition autoregression (STAR), standard asymptotic distribution results do not apply since nuisance parameters in the model are unidentified under the null hypothesis. The prevailing test of Luukkonen, Saikkonen and Teräsvirta (1988) is based on a linearization, which may adversely affect its power. This paper discusses an alternative procedure, based on a parametric bootstrap of a likelihood ratio test statistic, and investigates its size and power properties by a small simulation study. The results, however, indicate that the power of the bootstrap test is inferior to that of the existing test.Linearity testing; smooth transition autoregression model; nuisance parameter; nonstandard testing problem; bootstrap test

Another Look At Swedish Business Cycles, 1861-1988

This paper considers nine long Swedish macroeconomic time series whose business cycle properties were discussed by Englund, Persson, and Svensson (1992) using frequency domain techniques. It is found by testing that all but two of the logarithmed and differenced series are nonlinear. The observed nonlinearity is characterized by STAR models. The statistical and dynamic properties of the estimated STAR models are investigated using, among other things, parametrically estimated `local' or `sliced' spectra. Cyclical variation at business cycle frequencies does not seem to be constant over time for all series, and it is difficult to find a `Swedish business cycle'. Only two series may be regarded as having genuinely asymmetric cyclical variation. Standard Granger noncausality tests are adapted to the nonlinear (STAR) case, and the null hypothesis of noncausality is tested for pairs of series. The results point at strong temporal interactions between series. They also indicate that the as..

MODELING ASYMMETRIES AND MOVING EQUILIBRIA IN UNEMPLOYMENT RATES

The paper discusses a simple univariate nonlinear parametric time-series model for unemployment rates, focusing on the asymmetry observed in many OECD unemployment series. The model is based on a standard logistic smooth transition autoregressive model for the first difference of unemployment, but it also includes a lagged level term. This model allows for asymmetric behavior by permitting local nonstationarity in a globally stable model. Linearity tests are performed for a number of quarterly, seasonally unadjusted, unemployment series from OECD countries, and linearity is rejected for a number of them. For a number of series, nonlinearity found by testing can be modeled satisfactorily by use of our smooth transition autoregressive model. The properties of the estimated models, including persistence of the shocks according to them, are illustrated in various ways and discussed. Possible existence of moving equilibria in series not showing asymmetry is investigated and modeled with another smooth transition autoregressive model.

Modeling Cyclical Asymmetries in European Imports

This paper applies smooth transition models to capture the nonlinear behavior in the imports data of six major European economies and to assess whether such nonlinearities are related to business cycle asymmetries. Two classes of switch between regimes are considered: endogenously determined transition that assumes nonlinearities are generated by idiosyncratic components specific to foreign trade, and exogenous transition based on GDP growth as a more direct indicator of the cyclical state of the economy. The results support the proposition that the dynamics of imports are nonlinear. In Belgium, France, Spain, and the United Kingdom, regimes change over the business cycle, while in Germany and Italy the switch between regimes is endogenous. National characteristics play a role in defining the position of extreme regimes, the smoothness of the transition, and local dynamics within each state. Copyright International Atlantic Economic Society 2005C32, E32, F15,