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QUANTILE DOUBLE AUTOREGRESSION

Published online by Cambridge University Press:  25 June 2021

Qianqian Zhu  and
Guodong Li
Qianqian Zhu*
Affiliation:
Shanghai University of Finance and Economics
Guodong Li
Affiliation:
University of Hong Kong
*
Address correspondence to Qianqian Zhu, School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China; e-mail: [email protected].
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Abstract

Many financial time series have varying structures at different quantile levels, and also exhibit the phenomenon of conditional heteroskedasticity at the same time. However, there is presently no time series model that accommodates both of these features. This paper fills the gap by proposing a novel conditional heteroskedastic model called “quantile double autoregression”. The strict stationarity of the new model is derived, and self-weighted conditional quantile estimation is suggested. Two promising properties of the original double autoregressive model are shown to be preserved. Based on the quantile autocorrelation function and self-weighting concept, three portmanteau tests are constructed to check the adequacy of the fitted conditional quantiles. The finite sample performance of the proposed inferential tools is examined by simulation studies, and the need for use of the new model is further demonstrated by analyzing the S&P500 Index.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 4 , August 2022 , pp. 793 - 839
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

We are grateful to the Editor, Co-Editor, Associate Editor, and three anonymous referees for their valuable comments and suggestions, which led to substantial improvement of this article. Zhu’s research was supported by an NSFC grant 12001355, Shanghai Pujiang Program 2019PJC051, and Shanghai Chenguang Program 19CG44. Li’s research was partially supported by a Hong Kong RGC grant 17304617 and an NSFC grant 72033002.

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