Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Isotopic examination of links between diet, social differentiation and DISH at the post-medieval Carmelite Friary of Aalst, Belgium

Stable isotope ratios (δ13C and δ15N) were measured in human burials from the post-medieval (16th–18th c. AD) Carmelite friary burial grounds at Aalst, a town in Flanders, Belgium. Dietary patterns of 39 adult individuals were analyzed, from a mixed monastic and lay population buried in three different locations, reflecting groups with differing social status. The data show significant variation in the consumption of perhaps meat, but certainly also marine protein between females and males. This result represents a remarkable continuity with medieval dietary patterns, suggesting that the social and economic changes of the early modern period had a limited effect on everyday life. When both sexes were examined together, individuals buried in the cloister garth consumed significantly less marine protein compared to people buried in the church, likely reflecting social stratification. No statistical differences were observed between isotopic values from the church and the cloister alley, suggesting a similarly diverse diet of the monastic part of the buried population and that of the richer lay population. Finally, the hypothesis that diffuse idiopathic skeletal hyperostosis (DISH) is linked to a diet rich in animal protein was tested. No systematic or statistically significant differences between pathological and non-pathological bones from the same individuals affected with DISH were observed, and no statistical differences were found between individuals with DISH and individuals without DISH