Residual-based test for Nonlinear Cointegration with application in PPPs

Nested by linear cointegration first provided in Granger (1981), the definition of nonlinear cointegration is presented in this paper. Sequentially, a nonlinear cointegrated economic system is introduced. What we mainly study is testing no nonlinear cointegration against nonlinear cointegration by residual-based test, which is ready for detecting stochastic trend in nonlinear autoregression models. We construct cointegrating regression along with smooth transition components from smooth transition autoregression model. Some properties are analyzed and discussed during the estimation procedure for cointegrating regression, including description of transition variable. Autoregression of order one is considered as the model of estimated residuals for residual-based test, from which the teststatistic is obtained. Critical values and asymptotic distribution of the test statistic that we request for different cointegrating regressions with different sample sizes are derived based on Monte Carlo simulation. The proposed theoretical methods and models are illustrated by an empirical example, comparing the results with linear cointegration application in Hamilton (1994). It is concluded that there exists nonlinear cointegration in our system in the final results.

Geoprocessing journey-to-work data : delineating commuting regions in Dalarna, Sweden

Delineation of commuting regions has always been based on statistical units, often municipalities or wards. However, using these units has certain disadvantages as their land areas differ considerably. Much information is lost in the larger spatial base units and distortions in self-containment values, the main criterion in rule-based delineation procedures, occur. Alternatively, one can start from relatively small standard size units such as hexagons. In this way, much greater detail in spatial patterns is obtained. In this paper, regions are built by means of intrazonal maximization (Intramax) on the basis of hexagons. The use of geoprocessing tools, specifically developed for the processing ofcommuting data, speeds up processing time considerably. The results of the Intramax analysis are evaluated with travel-to-work area constraints, and comparisons are made with commuting fields, accessibility to employment, commuting flow density and network commuting flow size. From selected steps in the regionalization process, a hierarchy of nested commuting regions emerges, revealing the complexity of commuting patterns.