Abstract
Let Xn = ∑j=-∞∞ a jεn-j, n≥ be a non-causal linear process with weights a j '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 √N central limit theorem for the partial sums SN=∑n=1N [K(Xn) - EK(Xn)].
| Original language | English |
|---|---|
| Pages (from-to) | 345-358 |
| Number of pages | 14 |
| Journal | Journal of Theoretical Probability |
| Volume | 18 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2005 Apr 1 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
- Statistics and Probability
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Asymptotic normality for non-linear functionals of non-causal linear processes with summable weights. / Cheng, Tsung-Lin; Ho, Hwai Chung.
In: Journal of Theoretical Probability, Vol. 18, No. 2, 01.04.2005, p. 345-358.Research output: Contribution to journal › Article
TY - JOUR
T1 - Asymptotic normality for non-linear functionals of non-causal linear processes with summable weights
AU - Cheng, Tsung-Lin
AU - Ho, Hwai Chung
PY - 2005/4/1
Y1 - 2005/4/1
N2 - Let Xn = ∑j=-∞∞ a jεn-j, n≥ be a non-causal linear process with weights a j '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 √N central limit theorem for the partial sums SN=∑n=1N [K(Xn) - EK(Xn)].
AB - Let Xn = ∑j=-∞∞ a jεn-j, n≥ be a non-causal linear process with weights a j '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 √N central limit theorem for the partial sums SN=∑n=1N [K(Xn) - EK(Xn)].
UR - http://www.scopus.com/inward/record.url?scp=18244397190&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18244397190&partnerID=8YFLogxK
U2 - 10.1007/s10959-005-3506-9
DO - 10.1007/s10959-005-3506-9
M3 - Article
VL - 18
SP - 345
EP - 358
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
SN - 0894-9840
IS - 2
ER -