摘要
用任意的一元函数代替常数作为线性自回归滑动平均(ARMA)模型中自回归项的系数,提出并研究一类新的非参数ARMA模型.首先研究该模型的概率性质,获得了该模型的平稳性条件.分别用局域线性回归和全局的最小二乘方法估计模型中的函数系数和参数,在函数系数的局域线性估计中,推广了一个GCV准则以选择最优的窗宽.为了检验特殊的参数化模型是否已经足够描述实际数据的动态结构,提出了一个Bootstrap检验方法.随机仿真的例子表明本文的估计和检验方法是正确的和可行性的.进一步,用该模型成功地分析了一个实际数据集.
A new class of nonparametric autoregressive moving average models,in which arbitrary univariate functions act aa the coefficients of autoregressive terms instead of constants,is proposed and discussed. The probabilistic property of the models is investigated and a stationay condition is derived. It provides global estimate for the parameters and local linear smoother for the functional coefficients in the models respectively. In particular,the optimal bandwith is selected via a modified generalized cross-validation criterion. A bootstrap test is applied to test whether the functional coefficients are some specified parametric forms. The feasibility and validity of the proposed methods are justified by simulated examples. A real data set is analyzed by the proposed models.
出处
《厦门大学学报（自然科学版）》
CAS
CSCD
北大核心
2006年第5期628-633,共6页
Journal of Xiamen University：Natural Science
