Time-series regressions including non-linear transformations of an integrated variable are not uncommon in various fields of economics. In particular, within the Environmental Kuznets Curve (EKC) literature, where the effect on the environment of income levels is investigated, it is standard...

We consider a Seemingly Unrelated Time Series Equations framework for the linear Almost Ideal Demand system. The framework is applied to a consumer demand system covering nine non-durable commodities. We test for demand homogeneity within a specification where the static linear Almost Ideal...

Campbell and Shiller (1987) proposed a graphical technique for the present value model which consists of plotting the spread and theoretical spread as calculated from the cointegrated vector autoregressive model. We extend these techniques to a number of rational expectation models and give a...

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian...

We interpret the linear relations from exact rational expectations models as restrictions on the parameters of the statistical model called the cointegrated vector autoregressive model for non-stationary variables. We then show how reduced rank regression, Anderson (1951), plays an important...

In this paper, we consider two bootstrap algorithms for testing unit roots under the condition that the observed process is unit root integrated. The first method consists of generating the resampled data after fitting an autoregressive model to the first differences of the observations. The...

In this note some problems of asymptotic inference in a class of non-stationary stochastic processes are considered. In particular, it is shown that no criterion based on the existence of uniformly most powerful tests over a local neighborhood can be used in this situation.

Some optimal inference results for a class of diffusion processes, including the continuous state branching process and the approximate Wright-Fisher model with selection, are derived. It is then showed how the theory of convergence of experiments, due to Le Cam, can be applied to derive...