含结构变点无限方差序列的伪回归检验

基于最小二乘回归理论,研究了含结构变点无限方差序列的伪回归检验.结果表明,对两列含结构变点无限方差序列进行线性回归分析时,当两序列尾部指数之和小于1.5时,无论结构变点位置是否相同,t检验统计量均发散,导致伪回归现象的出现.究其原因,结构变点增加了回归误差的持久性,从而产生伪回归.蒙特卡罗数值模拟结果表明,伪回归现象不仅受序列尾部指数的影响,且对结构变点的位置敏感.

Spurious Regression Tests for Infinite-Variance Sequence with Structural Breaks

This paper analyzed a spurious regression involving infinite-variance processes in the presence of structural breaks by the least squares method using asymptotic theory. It is found that, when we regress two independent infinite-variance sequences with breaks in the level and the sum of tail indexes of the two sequences is less than 1.5, no matter whether the breaks occur at different points or not, the t-ratios become divergent and spurious phenomenon happens. The intuition behind this is that structural breaks can increase persistency in the level of regression errors, which then leads to spurious regressions. Simulation reveals that the effects of spurious regression depend on the tailed index, and to the relative location of breaks with the sample. As a result, spurious rejects might occur more often than what previously believed that they can arise even between infinite-variance series with structural breaks.