ASYMPTOTIC ESTIMATION THEORY FOR TIME SERIES REGRESSION MODELS WITH MULTIPLE CHANGE POINTS

ASYMPTOTIC ESTIMATION THEORY FOR TIME SERIES REGRESSION MODELS WITH MULTIPLE CHANGE POINTS
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多变点时间序列回归模型的渐近估计理论

DOI：
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发表时间：
2003
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通讯作者：
Takayuki Shiohama
Takayuki Shiohama
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文献类型：
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作者：
Takayuki Shiohama

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本文讨论了残差过程为圆形ARMA模型，且趋势函数满足一类Griander条件的时间序列回归模型的趋势函数中多个变点的估计问题。首先，给出了相邻假设之间似然比的渐近表示。得到了回归系数和变点的极大似然估计(MLE)和贝叶斯估计(BE)的极限分布。结果表明，边界元是渐近等价的，而最大似然估计不是一般意义上的。
This paper discusses the problem of estimating multiple change points in the trend function of a time series regression model where the residual process is a circular ARMA model, and the trend function satis es a sort of Grenander's conditions. First, the asymptotic representation of the likelihood ratio between contiguous hypothesis is given. Then the limiting distributions of the maximum likelihood estimator (MLE) and the Bayes estimator (BE) for the regression coeÆcients and change points are derived. It is seen that the BE is asymptotically eÆcient, and that the MLE is not so generally.