Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

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.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.

Detection of clinical mastitis with the help of a thermal camera

Increasing dairy farm size and increase in automation in livestock production require that new methods are used to monitor animal health. In this study, a thermal camera was tested for its capacity to detect clinical mastitis. Mastitis was experimentally induced in 6 cows with 10 mu g of Escherichia coli lipopolysaccharide (LPS). The LPS was infused into the left forequarter of each cow, and the right forequarters served as controls. Clinical examination for systemic and local signs and sampling for indicators of inflammation in milk were carried out before morning and evening milking throughout the 5-d experimental period and more frequently on the challenge day. Thermal images of experimental and control quarters were taken at each sampling time from lateral and medial angles. The first signs of clinical mastitis were noted in all cows 2 h postchallenge and included changes in general appearance of the cows and local clinical signs in the affected udder quarter. Rectal temperature, milk somatic cell count, and electrical conductivity were increased 4 h postchallenge and milk N-acetyl-beta-D-glucosaminidase activity 8 h postchallenge. The thermal camera was successful in detecting the 1 to 1.5 degrees C temperature change on udder skin associated with clinical mastitis in all cows because temperature of the udder skin of the experimental and control quarters increased in line with the rectal temperature. Yet, local signs on the udder were seen before the rise in udder skin and body temperature. The udder represents a sensitive site for detection of any febrile disease using a noninvasive method. A thermal camera mounted in a milking or feeding parlor could detect temperature changes associated with clinical mastitis or other diseases in a dairy herd.

Elliptic flow of thermal photons in heavy-ion collisions at Relativistic Heavy Ion Collider and Large Hadron Collider

We calculate the thermal photon transverse momentum spectra and elliptic flow in $\sqrt{s_{NN}} = 200$ GeV Au+Au collisions at RHIC and in $\sqrt{s_{NN}} = 2.76$ TeV Pb+Pb collisions at the LHC, using an ideal-hydrodynamical framework which is constrained by the measured hadron spectra at RHIC and LHC. The sensitivity of the results to the QCD-matter equation of state and to the photon emission rates is studied, and the photon $v_2$ is discussed in the light of the photonic $p_T$ spectrum measured by the PHENIX Collaboration. In particular, we make a prediction for the thermal photon $p_T$ spectra and elliptic flow for the current LHC Pb+Pb collisions.