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NONSTATIONARY LINEAR PROCESSES WITH INFINITE VARIANCE GARCH ERRORS

Published online by Cambridge University Press:  26 October 2020

Rongmao Zhang  and
Ngai Hang Chan
Rongmao Zhang
Affiliation:
Zhejiang University
Ngai Hang Chan*
Affiliation:
Southwestern University of Finance The Chinese University of Hong Kong
*
Address correspondence to Ngai Hang Chan, Department of Statistics, The Chinese University of Hong Kong, Hong Kong; e-mail: nhchan@sta.cuhk.edu.hk.
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Abstract

Recently, Cavaliere, Georgiev, and Taylor (2018, Econometric Theory 34, 302–348) (CGT) considered the augmented Dickey–Fuller (ADF) test for a unit-root model with linear noise driven by i.i.d. infinite variance innovations and showed that ordinary least squares (OLS)-based ADF statistics have the same distribution as in Chan and Tran (1989, Econometric Theory 5, 354–362) for i.i.d. infinite variance noise. They also proposed an interesting question to extend their results to the case with infinite variance GARCH innovations as considered in Zhang, Sin, and Ling (2015, Stochastic Processes and their Applications 125, 482–512). This paper addresses this question. In particular, the limit distributions of the ADF for random walk models with short-memory linear noise driven by infinite variance GARCH innovations are studied. We show that when the tail index $\alpha <2$ , the limit distributions are completely different from that of CGT and the estimator of the parameters of the lag terms used in the ADF regression is not consistent. This paper provides a broad treatment of unit-root models with linear GARCH noises, which encompasses the commonly entertained unit-root IGARCH model as a special case.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 5 , October 2021 , pp. 892 - 925
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

We would like to thank the Editor, Professor Peter C.B. Phillips and the Co-Editor, Professor G. Cavaliere, and two anonymous referees for their critical comments and thoughtful suggestions, which led to a much improved version of this paper. Research supported in part by grants from NSFC (No. 11771390/11371318), the USyd-ZJU Partnership Collaboration Awards and the Fundamental Research Funds for the Central Universities (Zhang) and HKSAR-RGC-GRF Nos 14308218 and 14325216 and HKSR-RGC-TRF No. T32-101/15-R (Chan).

References

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