固定设计下时间序列非参数回归模型的方差变点检验

Test for Variance Change in Time Series Model under Fixed Design Regression

研究固定设计下时间序列非参数回归模型的方差变点检验问题,基于Beta-Bernstein方法估计模型中回归函数,利用残差序列构造CUSUM检验统计量,在一定条件下证明了在原假设下检验统计量收敛于Brown桥的上确界,最后通过数值模拟验证检验方法的有效性.

Detection problem of variance change in time series model under fixed design regression was studied. Beta-Bernstein smoothing was used for estimating regression function, the residual sequence was obtained and CUSUM of square test statistics was established. It was shown that the distribution of the test statistics converges at the supremum of a standard Brown bridge under certain conditions. The perform- ance of the method was illustrated by simulation studies.