The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

Selenium and its effects on growth, yield and tuber quality in potato

Selenium (Se) has been demonstrated to be an essential trace element for maintenance of animal and human health. Although it has not been confirmed to be an essential micronutrient in higher plants, there is increasing evidence that Se functions as an antioxidant in plants. Selenium has been shown to exert a beneficial effect on crop growth and promotes stress tolerance at low concentrations. However, the specific physiological mechanisms that underlie the positive effects of Se in plants have not been clearly elucidated. The aims of this study were to determine the Se concentration in potato (Solanum tuberosum L.) and the effects of Se on the accumulation of carbohydrates, growth and yield in potato plants. An additional aim was to study the impact of Se on the total glycoalkaloid concentration in immature potato tubers. The distribution of Se in different biochemical Se fractions and the effect of storage on the Se concentration were studied in Se-enriched tubers. Furthermore, the effect of Se on raw darkening and translocation of Se from seed tubers to the next tuber generation was investigated. Due to the established anti-ageing properties of Se, it was of interest to study if Se affects physiological age and growth vigour of seed tubers. The Se concentrations in the upper leaves, roots, stolons and tubers of potato increased with increasing Se supplementation. The highest Se concentration was reached in young upper leaves, roots and stolons, indicating that added selenate was efficiently utilized and taken up at an early stage. During the growing period the Se concentration declined in the aerial parts, roots and stolons of potato plants whereas an intensive accumulation took place in immature and mature tubers. Selenium increased carbohydrate accumulation in the young upper leaves and in stolons, roots and tubers at maturity. This could not be explained by increased production of photoassimilates as net photosynthesis did not differ among Se treatments. The Se treated plants produced higher tuber yields than control plants, and at the highest Se concentration (0.3 mg kg-1) lower numbers of larger tubers were harvested. Increased yield of Se treated plants suggested that Se may enhance the allocation of photoassimilates for tuber growth, acting as a strong sink for both Se and for carbohydrates. Similarly as for other plant species, the positive impact of Se on the yield of potato plants could be related to its antioxidative effect in delaying senescence. The highest Se supplementation (0.9 mg kg-1) slightly decreased the glycoalkaloid concentration of immature tubers. However, at this level the Se concentration in tubers was about 20 µg g-1 DW. A 100 g consumption of potato would provide about 500 mg of Se, which exceeds the upper safe intake level of 400 µg per day for human dietary. The low Se applications (0.0035 and 0.1 mg kg-1) diminished and retarded the degree of raw darkening in tubers stored for one and eight months, which can be attributed to the antioxidative properties of Se. The storage for 1 to 12 months did not affect the Se concentrations of tubers. In the Se enriched tubers Se was allocated to the organic Se fraction, indicating that it was incorporated into organic compounds in tubers. Elevated Se concentration in the next-generation tubers produced by the Se enriched seed tubers indicated that Se could be translocated from the seed tubers to the progeny. In the seed tubers stored for 8 months, at high levels, Se had some positive effects on the growth vigour of sprouts, but Se had no consistent effect on the growth vigour of seed tubers of optimal physiological age. These results indicate that Se is a beneficial trace element in potato plants that exerts a positive effect on yield formation and improves the processing and storage quality of table potato tubers. These positive effects of Se are, however, dependent on the Se concentration and the age of the potato plant and tuber.

Practical Proposals for Specifying k-Nearest Neighbours Weights Matrices

In this article we introduce and evaluate testing procedures for specifying the number k of nearest neighbours in the weights matrix of spatial econometric models. The spatial J-test is used for specification search. Two testing procedures are suggested: an increasing neighbours testing procedure and a decreasing neighbours testing procedure. Simulations show that the increasing neighbours testing procedures can be used in large samples to determine k. The decreasing neighbours testing procedure is found to have low power, and is not recommended for use in practice. An empirical example involving house price data is provided to show how to use the testing procedures with real data.