Statistic inference for a single-index ARCH-M model

Qiang Xiong, Zhiyong Hu and Yuan Li

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 1, 102-117

Abstract: For a single-index autoregressive conditional heteroscedastic (ARCH-M) model, estimators of the parametric and non parametric components are proposed by the profile likelihood method. The research results had shown that all the estimators have consistency and the parametric estimators have asymptotic normality. We extend this line of research by deriving the asymptotic normality of the non parametric estimator. Based on the asymptotic properties, we propose Wald statistic and generalized likelihood ratio statistic to investigate the testing problems for ARCH effect and goodness of fit, respectively. A simulation study is conducted to evaluate the finite-sample performance of the proposed estimation methodology and testing procedure.

Date: 2018
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DOI: 10.1080/03610926.2017.1300283

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