期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2006
卷号：68
期号：04
出版社：Indian Statistical Institute
摘要：We consider parameter estimation for a class of ARCH$(\infty)$ models, which do not necessarily have a parametric form. The estimation is based on a normalized least squares approach, where the normalization is the weighted sum of past observations. The number of parameters estimated depends on the sample size and increases as the sample size grows. Using maximal inequalities for martingales and mixingales we derive a uniform rate of convergence for the parameter estimator. We show that the rate of convergence depends both on the number of parameters estimated and the rate that the ARCH$(\infty)$ parameters tend to zero.
关键词：ARCH, maximal inequalities, nonlinear process, near epoch dependence,weighted least squares.
