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-autocorrelation consistent (HAC) 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 US house prices illustrate the relevance of the advocated method in practice.
About the Speaker:
Xuewen Yu is currently an Assistant Professor of Economics at the Department of Applied Economics, School of Management, Fudan University. He obtained a Ph.D. in Economics from Purdue University in August 2022, an M.S. in Statistics and a B.S. in Finance from the University of Science and Technology of China in 2016 and 2014, respectively. His research interests include Econometric Theory, Financial Econometrics, and Empirical Macroeconomics. His papers have appeared in Journal of Econometrics, Econometrics Journal, Journal of Economic Dynamics and Control, Journal of Time Series Analysis . He has also served as a referee for several econometrics journals such as JoE, JBES, ER , among others. His work has been awarded the 2021 Denis Sargan Econometric Prize by the Royal Economics Society.
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