Asymptotic normality for non-linear functionals of non-causal linear processes with summable weights

Tsung Lin Cheng; Hwai Chung Ho

doi:10.1007/s10959-005-3506-9

Asymptotic normality for non-linear functionals of non-causal linear processes with summable weights

Tsung Lin Cheng, Hwai Chung Ho

Graduate Institute of Statistics and Information Science

Research output: Contribution to journal › Article

4 Citations (Scopus)

Abstract

Let X_n = ∑_j=-∞^∞ a _jε_n-j, n≥ 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 √N central limit theorem for the partial sums S_N=∑_n=1^N [K(X_n) - EK(X_n)].

Original language	English
Pages (from-to)	345-358
Number of pages	14
Journal	Journal of Theoretical Probability
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s10959-005-3506-9
Publication status	Published - 2005 Apr 1

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All Science Journal Classification (ASJC) codes

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

Cite this

Cheng, T. L., & Ho, H. C. (2005). Asymptotic normality for non-linear functionals of non-causal linear processes with summable weights. Journal of Theoretical Probability, 18(2), 345-358. https://doi.org/10.1007/s10959-005-3506-9

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10.1007/s10959-005-3506-9