基于一种分块经验似然方法的ARMA模型的参数推断

Inference for ARMA Models Based on A Progressive Block Empirical Likelihood Method

Owen在1988年提出了经验似然方法,这是一种非参数或半参数的统计推断方法,具有非参数方法的可靠性、灵活性和似然方法的有效性等良好的统计性质.经验似然统计推断方法多用于独立同分布数据的参数推断,而对于不独立的数据,例如时间序列这种存在相依性关系的数据,则不能直接使用经验似然推断.对于存在相依关系的时间序列数据的经验似然推断,在时域中一般采用分块的方式消除相依关系,再使用经验似然方法进行推断,而分块的块长对估计的效果有很大的影响,但至今,关于最优的分块块长的选择还存在很多问题.本文主要研究了一种不需要选择块长的分块经验似然推断方法——"PBEL",并使用该方法研究了ARMA模型的经验似然参数推断问题,并与极大似然估计作了比较.

Empirical likelihood method is a kind of parametric or non-parametric statistical inference method proposed by Owen in 1988. It has many good statistical properties,such as the reliability as a non-parametric method,flexibility,effective as a likelihood method and so on. But empirical likelihood is applied in independent identical data,it can't be used directly in dependent data,such as time series. For the serial correlation models,we can block the data in order to get independent and identical data blocks( Kitamura,1997). In this way,we can use the empirical likelihood to estimate parameters in time domain. But the length of the blocks has a great influence on the result of the inference. In this paper,a progressive block empirical likelihood method called"PBEL"( Nordman,2013) which does not require a block length choice,is used for the inference of ARMA models and compared with maximum likelihood estimation.