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

Tsung-Lin Cheng () and Hwai-Chung Ho ()
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Tsung-Lin Cheng: National Changhua University of Education
Hwai-Chung Ho: Academia Sinica

Journal of Theoretical Probability, 2005, vol. 18, issue 2, 345-358

Abstract: 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 a j ’s satisfying certain summability conditions, and the iid sequence of innovation {ε i } 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 (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10959-005-3506-9

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