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本文將Phillips and Han (2008)之一階差分估計式推展至有時間趨勢之一階自我 迴歸模型的估計與推論上。藉由簡易的去除時間趨勢過程, 一階差分估計式仍具 有漸近常態分配的性質; 同時, 據以建構之單根檢定相較於以雙重差分估計式為 基礎之單根檢定更有檢定力。本文提出的方法在固定效果動態追蹤資料模型下更 具應用價值

This study applies nonlinear KSS unit root test (Kapetanios, Shinb, and Snell, 2003) and an Asymmetric Exponential Smooth Transition Auto-Regressive (AESTAR) unit root test, proposed by Sollis (2009), to investigate the validity of long-run Purchasing Power Parity (PPP) for six high-growth countries. The empirical results indicate that PPP holds for five of the six high-growth countries studied, namely Brazil, China, Indonesia, Mexico and South Korea, using the KSS test. Furthermore, using Sollis (2009) AESTAR unit root test reveals that real appreciations in the value of the Indonesia Rupiah-U.S. and Korea Won-U.S. dollar exchange rate are slower to revert do the mean (nonlinearly) than depreciations of the same proportionate amount, and the adjustment toward PPP is found to be nonlinear and asymmetric. On the other hand, Brazil/USD, China/USD and Mexico/USD adjustments are found to be nonlinear and symmetric. The governments of these five countries can use PPP to determine whether a currency is overvalued or undervalued, as well as if the country is experiencing differences between domestic and foreign inflation rates. These results have important policy implications for the emerging high-growth economies in this study.

We consider the Borcherds-Cartan matrix obtained from a symmetrizable generalized Cartan matrix by adding one imaginary simple root. We extend the result of Gebert and Teschner [Lett. Math. Phys., 1994, 31: 327-334] to the quantum case. Moreover, we give a connection between the irreducible dominant representations of quantum Kac-Moody algebras and those of quantum generalized Kac-Moody algebras. As the result, a large class of irreducible dominant representations of quantum generalized Kac-Moody algebras were obtained from representations of quantum Kac-Moody algebras through tensor algebras.