Tests for Long-Run Granger Non-Causality in Cointegrated Systems

In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. A test for the ranks of submatrices of the cointegration matrix and its orthogonal matrix plays a vital role in the former. The relevant small sample experiments indicate that the proposed method performs reasonably well in finite samples. As empirical applications, we examine long-run causal relations among long-term interest rates of three and five nations.Vector autoregression, Cointegration, Long-run causality, Hypothesis testing

Tests for Long-Run Granger Non-Causality in Cointegrated Systems

In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. A test for the ranks of submatrices of the cointegration matrix and its orthogonal matrix plays a vital role in the former. The relevant small sample experiments indicate that the proposed method performs reasonably well in finite samples. As empirical applications, we examine long-run causal relations among long-term interest rates of three and five nations.Vector autoregression, Cointegration, Long-run causality, Hypothesis testing

A review of biomechanics of the shoulder and biomechanical concepts of rotator cuff repair

AbstractIn this article, we describe the basic knowledge about shoulder biomechanics, which is thought to be useful for surgeons. Some clinical reports have described that the excellent outcome after cuff repair without acromioplasty and a limited acromioplasty might be enough for subacromial decompression. It was biomechanically demonstrated that a 10-mm medial shift of the tendon repair site has a minimum effect on biomechanics. Many biomechanical studies reported that the transosseous equivalent repair was superior to other techniques, although the tendon may lose its inherent elasticity. We herein introduce our recent experiment data and latest information on biomechanics