Are the Unit-Root Tests Adequate for Nonlinear Models?
In the previous chapter, we surveyed some basic results achieved in the literature about nonstationary and nonlinear time series models. The motivation of this chapter is to consider these notions together. Indeed, as suggested in chapter 1, many economic time series display both nonlinear and nonstationary behavior and it seems a natural approach to consider them together. As a starting point, we ask the following question. Consider a nonstationary variable x t . What are the properties of the nonlinear model x t = f (x t−1,..., x t−p ) + ε t generating x t ? It is impossible to give a general answer without specifying the exact form of the function f. In the sequel, we shall adopt an empirical approach and consider nonlinear processes currently used in the different fields of applied economics. However, this is not enough if we want to answer our question. We also need enquiring about the type of nonstationarity that is produced by nonlinear models. In general terms, the fact that a process has no stationary asymptotic distribution is due to several causes.
KeywordsRandom Walk Unit Root Nonlinear Transformation Monte Carlo Experiment Bilinear Model
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