基于傅里叶变换的含确定性趋势结构突变的协整回归模型和不等方差检验

一般来说，数据结构突变点的位置是未知的或突变点的存在性无法准确预知。Enders和Lee（2009，2011）1]2]证明低频的傅里叶变换（Fourier transformation）就能较精确地处理单位根检验中的数据结构突变（异质结构突变）问题。本文在协整模型框架下，使用傅里叶变换处理协整模型确定性趋势项下的结构突变，考察了协整模型参数的收敛速度，并重新推导了不等方差检验。傅里叶近似项参数的收敛速度为： 。使用蒙特卡洛模拟表明：在缺乏结构突变的先验知识的情况下，使用低频的傅里叶变换能较好地处理协整回归中的确定性趋势的结构突变的问题，显著提高协整向量的估计效率。使用改进后的方法，重新研究了中国股市和国际股市联动关系的密切程度，实证结果更为强烈地支持：中国投资者投资于澳大利亚市场分散风险的收益显著弱于投资其他国际市场。

The cointegration regression model with deterministic trend breaks and the Equal variance test based on Fourier transformation

Generally speaking, the location of the structural breaks in DGP and the existence of structural break are uncertain. Enders and Lee (2009, 2011) show that, in the unit root tests, （heterogeneous）structural changes of unknown form in the data can be captured well using the low frequency components of Fourier approximation. Under the cointegration framework, we examine the convergence rate of the parameters and re-derive the unequal variance test with breaks in the deterministic trend. Our results show that the terms containing Fourier approximation in the regression model converge at the rate . Our simulations show that the efficiency of cointegration vector estimation can be enhanced significantly when we use Fourier approximation to model the unknown-form structural breaks in the deterministic trend in the cointegration regression model. This paper re-examines the comovement patterns between China capital market and other international markets using the improved method. The empirical results suggest strongly that Chinese investors can benefit less from investing in Australia other international markets.