Unit root testing under a local break in trend using partial information on the break date*

We consider unit root testing allowing for a break in trend when partial information is available regarding the location of the break date. This takes the form of knowledge of a relatively narrow window of data within which the break takes place, should it occur at all. For such circumstances, we suggest employing a union of rejections strategy, which combines a unit root test that allows for a trend break somewhere within the window, with a unit root test that makes no allowance for a trend break. Asymptotic and _nite sample evidence shows that our suggested strategy works well, provided that, when a break does occur, the partial information is correct. An empirical application to UK interest rate data containing the 1973 ‘oil shock’ is also considered

Quantum entanglement of charges in bound states with finite-size dyons

We show that the presence of finite-size monopoles can lead to a number of interesting physical processes involving quantum entanglement of charges. Taking as a model the classical solution of the N=2 SU(2) Yang-Mills theory, we study interaction between dyons and scalar particles in the adjoint and fundamental representation. We find that there are bound states of scalars and dyons, which, remarkably, are always an entangled configuration of the form |\psi > =|dyon+> |scalar-> +/- |dyon->|scalar+>. We determine the energy levels and the wave functions and also discuss their stability.Comment: 29 pages, 3 figures. Minor correction in references (to appear in JHEP04 (2002) 010

Testing for unit roots under multiple possible trend breaks and non-stationary volatility using bootstrap minimum Dickey-Fuller statistics

In a recent paper, Harvey et al. (2013) [HLT] propose a new unit root test that allows for the possibility of multiple breaks in trend. Their proposed test is based on the infimum of the sequence (across all candidate break points) of local GLS detrended augmented Dickey-Fuller-type statistics. HLT show that the power of their unit root test is robust to the magnitude of any trend breaks. In contrast, HLT show that the power of the only alternative available procedure of Carrion-i-Silvestre et al. (2009), which employs a pre-test-based approach, can be very low indeed (even zero) for the magnitudes of trend breaks typically observed in practice. Both HLT and Carrion-i-Silvestre et al. (2009) base their approaches on the assumption of homoskedastic shocks. In this paper we analyse the impact of non-stationary volatility (for example single and multiple abrupt variance breaks, smooth transition variance breaks, and trending variances) on the tests proposed in HLT. We show that the limiting null distribution of the HLT unit root test statistic is not pivotal under non- stationary volatility. A solution to the problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice. A number of dfferent possible implementations of the bootstrap algorithm are discussed

Challenging lanthanide relaxation theory: erbium and thulium complexes that show NMR relaxation rates faster than dysprosium and terbium analogues

Measurements of the proton NMR paramagnetic relaxation rates for several series of isostructural lanthanide(III) complexes have been performed in aqueous solution over the field range 1.0 to 16.5 Tesla. The field dependence has been modeled using Bloch–Redfield–Wangsness theory, allowing values for the electronic relaxation time, Tle and the magnetic susceptibility, μeff, to be estimated. Anomalous relaxation rate profiles were obtained, notably for erbium and thulium complexes of low symmetry 8-coordinate aza-phosphinate complexes. Such behaviour challenges accepted theory and can be interpreted in terms of changes in Tle values that are a function of the transient ligand field induced by solvent collision and vary considerably between Ln3+ ions, along with magnetic susceptibilities that deviate significantly from free-ion values

Testing the Order of Fractional Integration of a Time Series in the Possible Presence of a Trend Break at an Unknown Point

We develop a test, based on the Lagrange multiplier [LM] testing principle, for the value of the long memory parameter of a univariate time series that is composed of a fractionally integrated shock around a potentially broken deterministic trend. Our proposed test is constructed from data which are de-trended allowing for a trend break whose (unknown) location is estimated by a standard residual sum of squares estimator. We demonstrate that the resulting LM-type statistic has a standard limiting null chi-squared distribution with one degree of freedom, and attains the same asymptotic local power function as an infeasible LM test based on the true shocks. Our proposed test therefore attains the same asymptotic local optimality properties as an oracle LM test in both the trend break and no trend break environments. Moreover, and unlike conventional unit root and stationarity tests, this asymptotic local power function does not alter between the break and no break cases and so there is no loss in asymptotic local power from allowing for a trend break at an unknown point in the sample, even in the case where no break is present. We also report the results from a Monte Carlo study into the finite-sample behaviour of our proposed test

Soil-landscape and climatic relationships in the middle Miocene of the Madrid Basin

The Miocene alluvial-lacustrine sequences of the Madrid Basin, Spain, formed in highly varied landscapes. The presence of various types of palaeosols allows assessment of the effects of local and external factors onsedimentation, pedogenesis and geomorphological development. In the northern, more arid, tectonicallyactive arca, soils were weakly developed in aggrading alluvial fans, dominated by mass flows. reflecting high sedimentation rates. In more distal parts of the fans and in playa lakes calcretes and dolocretes developed: the former were associated with Mg-poor fan sediments whitc: the latter formed on Mg-rich lake clays exposed during minar lake lowstands. The nonh-east part of the basin had a less arid climate. Alluvial fans in this area were dominated by stream Aood deposits, sourced by carbonate terrains. Floodplain and freshwater lakc deposits formed in distal areas. The high local supply of calcium carbonate may have contributed to the preferential developmenl on calcretes on the fans. Both the fan and floodplain palaeosols exhibit pedofacies relationships and more mature soils developed in settings more distant from the sediment sources. Palaeosols also developed on pond and lake margin carbonates, and led to the formation of palustrine limestones. The spatial distributions and stratigraphies of palaeosols in the Madrid Basin alluvial fans suggest that soil formation was controlled by local factors. These palaeosols differ from those seen in Quatemary fans. Which are characterized by climatically induced periods of stability and instability

Robust tests for a linear trend with an application to equity indices

In this paper we develop a testing procedure for the presence of a deterministic linear trend in a univariate time series which is robust to whether the series is I(0) or I(1) and requires no knowledge of the form of weak dependence present in the data. Our approach is motivated by the testing procedures of Vogelsang [1998, Econometrica, vol 66, p123–148] and Bunzel and Vogelsang [2005, Journal of Business and Economic Statistics, vol 23, p381–394], but utilises an auxiliary unit root test to switch between critical values in the exact I(1) and I(0) environments, rather than using this unit root test to scale the test statistic as is done in the aforementioned procedures. We show that our proposed tests have uniformly greater local asymptotic power than the tests of Vogelsang (1998) and Bunzel and Vogelsang (2005) when the error process is exact I(1), identical local asymptotic when the error process is I(0), and have better overall local asymptotic power when the error process is near I(1). Our proposed tests also display superior finite sample power to the tests of Vogelsang (1998) and Bunzel and Vogelsang (2005) and are competitive in finite samples with tests designed to be optimal in both the exact I(1) and I(0) environments. We apply our test procedures to a number of equity indices and find that these series appear to have a significant upward deterministic trend, yet are also highly persistent about this long run growth path

Correlates of light and moderate-to-vigorous objectively measured physical activity in four-year-old children

Correlates of physical activity (PA) are hypothesized to be context and behaviour specific, but there is limited evidence of this in young children. The aim of the current study is to investigate associations between personal, social and environmental factors and objectively measured light and moderate-to-vigorous PA (LPA and MVPA, respectively) in four-year-old children.Cross-sectional data were used from the Southampton Women's Survey, a UK population-based longitudinal study. Four-year old children (n = 487, 47.0% male) had valid PA data assessed using accelerometry (Actiheart) and exposure data collected with a validated maternal questionnaire (including data on child personality, family demographics, maternal behaviour, rules and restrictions, and perceived local environment). Linear regression modelling was used to analyse associations with LPA and MVPA separately, interactions with sex were explored.LPA minutes were greater in children whose mothers reported more PA (vs. inactive: regression coefficient±standard error: 6.70±2.94 minutes), and without other children in the neighbourhood to play with (-6.33±2.44). MVPA minutes were greater in children with older siblings (vs. none: 5.81±2.80) and those whose mothers used active transport for short trips (vs. inactive: 6.24±2.95). Children accumulated more MVPA in spring (vs. winter: 9.50±4.03) and, in boys only, less MVPA with availability of other children in the neighbourhood (-3.98±1.70).Young children's LPA and MVPA have differing associations with a number of social and environmental variables. Interventions targeting PA promotion in young children outside of formal care settings should consider including intensity specific factors