Nonlinear dynamics and smooth transition models

Sammanfattning: During the last few years nonlinear models have been a very active area of econometric research: new models have been introduced and existing ones generalized. To a large extent, these developments have concerned models in which the conditional moments are regime-dependent. In such models, the different regimes are usually linear and the change between them is governed by an observable or unobservable variable. These specifications can be useful in situations in which it is suspected that the behaviour of the dependent variable may vary between regimes. A classical example can be found the business cycle literature where it is argued that contractions in the economy are not only more violent but also short-lived than expansions. Unemployment, which tends to rise faster during recessions than decline during booms, constitutes another example. Two of the most popular regime-dependent models are the smooth transition and the threshold model. In both models cases the transition variable is observable but the specification of the way in which the model changes from one regime to the other is different. Particularly, in the smooth transition model the change is a continuous whereas in the threshold model it is abrupt. One of the factors that has influenced the development of nonlinear models are improvements in computer technology. They have not only permitted an introduction of more complex models but have also allowed the use of computer-intensive methods in hypothesis testing. This is particularly important in nonlinear models because there these methods have proved to be practical in testing statistical hypothesis such as linearity and parameter constancy. In general, these testing situation are not trivial and their solution often requires computer-intensive methods. In particular, bootstrapping and Monte Carlo testing are now commonly used. In this thesis the smooth transition model is used in different ways. In the first chapter, a vector smooth transition model is used as a device for deriving a test for parameter constancy in stationary vector autoregressive models. In the second chapter we introduce a panel model whose parameters can change in a smooth fashion between regimes as a function of an exogenous variable. The method is used to investigate whether financial constraints affect firms' \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ investment decisions. The third chapter is concern with linearity testing in smooth transition models. New tests are introduced and Monte Carlo testing techniques are shown to be useful in achieving control over the size of the test. Finally, the last chapter is devoted to the Smooth Permanent Surge model. This is a nonlinear moving average model in which a shock can have transitory or permanent effects depending on its sign and magnitude. Test for linearity and random walk hypothesis are introduced.