Journal of Theoretical Probability

, Volume 18, Issue 2, pp 345–358 | Cite as

Asymptotic Normality for Non-linear Functionals of Non-causal Linear Processes with Summable Weights

Article

Abstract

Let \(X_{n} = \sum\limits{_{j = - \infty }^\infty} {a_{j}ε _{n - j,} n\geq 1,}\) be a non-causal linear process with weights aj’s satisfying certain summability conditions, and the iid sequence of innovation {εi} having zero mean and finite second moment. For a large class of non-linear functional K which includes indicator functions and polynomials, the present paper develops the \( \sqrt N\) central limit theorem for the partial sums \( S_N = \sum\limits{_{n = 1}^N} {\left[ {K(X_n ) - EK(X_n )} \right].}\)

Keywords

Central limit theorem non-causal stationary process non- linear functional 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsNational Changhua University of EducationTaiwanROC
  2. 2.Institute of Statistical ScienceAcademia SinicaTaiwan

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