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INFERENCE IN MILDLY EXPLOSIVE AUTOREGRESSIONS UNDER UNCONDITIONAL HETEROSKEDASTICITY

Published online by Cambridge University Press:  18 September 2024

Xuewen Yu Open the ORCID record for Xuewen Yu [Opens in a new window]  and
Mohitosh Kejriwal Open the ORCID record for Mohitosh Kejriwal [Opens in a new window]
Xuewen Yu*
Affiliation:
Fudan University
Mohitosh Kejriwal
Affiliation:
Purdue University
*
Address correspondence to Xuewen Yu, Department of Applied Economics, School of Management, Fudan University, 670 Guoshun Road, Shanghai, China; e-mail: xuewenyu@fudan.edu.cn.
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Abstract

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Mildly explosive autoregressions have been extensively employed in recent theoretical and applied econometric work to model the phenomenon of asset market bubbles. An important issue in this context concerns the construction of confidence intervals for the autoregressive parameter that represents the degree of explosiveness. Existing studies rely on intervals that are justified only under conditional homoskedasticity/heteroskedasticity. This paper studies the problem of constructing asymptotically valid confidence intervals in a mildly explosive autoregression where the innovations are allowed to be unconditionally heteroskedastic. The assumed variance process is general and can accommodate both deterministic and stochastic volatility specifications commonly adopted in the literature. Within this framework, we show that the standard heteroskedasticity- and autocorrelation-consistent estimate of the long-run variance converges in distribution to a nonstandard random variable that depends on nuisance parameters. Notwithstanding this result, the corresponding t-statistic is shown to still possess a standard normal limit distribution. To improve the quality of inference in small samples, we propose a dependent wild bootstrap-t procedure and establish its asymptotic validity under relatively weak conditions. Monte Carlo simulations demonstrate that our recommended approach performs favorably in finite samples relative to existing methods across a wide range of volatility specifications. Applications to international stock price indices and U.S. house prices illustrate the relevance of the advocated method in practice.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 36
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

We are grateful to Peter Phillips (the Editor), Xu Cheng (the Co-Editor), four anonymous referees, Yong Bao, Giuseppe Cavaliere, Prosper Dovonon, Pierre Perron, Yundong Tu, and Alan Wan, as well as seminar participants at City University of Hong Kong, Concordia University, Fudan University, Nanyang Technological University, Peking University, University of Exeter, University of Illinois Urbana–Champaign, and University of Science and Technology of China, for their comments that improved the paper substantially. Yu is supported by Shanghai Sailing Program No. 23YF1402000 and the National Natural Science Foundation of China (Grant No. 72303040). Any errors are our own.

References

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