Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models

Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (4): 617-622.

Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models

Department of Applied Mathematics Northwestern Polytechnical University,Department of Applied Mathematics,Northwestern Polytechnical University,Department of Applied Mathematics,Northwestern Polytechnical University,,Xi’an 710072,China,Xi’an 710072,China National Key Laboratory of Pattern Recognition,Beijing 100080,China Institute of Automation,Chinese Academy of Sciences,Beijing 100080,China,Xi’an 710072,China

Received:2005-10-10 Online:2006-12-30 Published:2023-11-23
About author:WU Xin-qian(1969-),male,native of Zhongmou,Henan,Ph.D.,engages in nonlinear time series analysis;TIAN Zheng(1948-),female,native ofFaku,Liaoning,a professor and tutor of doctor student of Northwestern Polytechnical University,engages in nonlinear time series analysis.
Supported by:
Supported by the National Natural Science Foundation of China(60375003)； Supported by the Chinese Aviation Foundation(03153059)；

Abstract

Abstract: Consider the model Y_t=βY_t-1+g(Y_t-2)+ε_tfor 3＜=t＜=T. Here g is an unknown function,βis an unknown parameter, vε_t are i.i.d,random errors with mean 0 and varianceσ2 and the fourth moment α_4,andεt are independent of Y_s for all t＞=3 and s=1,2. Pseudo-LS estimators ... distribution to N(0,1). The result can be used to establish large sample interval estimates of σ² or to make large sample tests for σ².

Key words: partly , linear , autoregressive , model;error , variance;piecewise , polynomial, pseudo-LS estimation;weak consistency;asymptotic normality

CLC Number:

O212.7

WU Xin-qian, TIAN Zheng, JU Yan-wei. Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(4): 617-622.

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Asymptotic Normality of Pseudo-LS Estimator of Error Variance in Partly Linear Autoregressive Models

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